{"id":722,"date":"2021-08-22T12:24:15","date_gmt":"2021-08-22T12:24:15","guid":{"rendered":"https:\/\/santoshdhamone.com\/?page_id=722"},"modified":"2024-01-07T06:18:00","modified_gmt":"2024-01-07T06:18:00","slug":"s-y-b-sc","status":"publish","type":"page","link":"https:\/\/santoshdhamone.com\/index.php\/s-y-b-sc\/","title":{"rendered":"S. Y. B. Sc."},"content":{"rendered":"\t\t
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S. Y. B. Sc.<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Linear Algebra II<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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 <\/h3>\n
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Course Code: USMT402<\/span><\/strong><\/h3>\n

Credits: 2 || Lecture\/week: 3<\/span><\/strong>
Probable\/Actual Hrs Available: 4<\/span><\/strong><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Unit i : linear transformation<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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NAME OF UNIT<\/p><\/div><\/div><\/td>

Titles \/ Details<\/p><\/div><\/div><\/td>

Video Lectures<\/p><\/div><\/div><\/td>

Lecture Notes<\/p><\/div><\/div><\/td>

Assignments \/ Practicals<\/p><\/div><\/div><\/td>

Ratings<\/p><\/div><\/div><\/td><\/tr>

Linear Transformation<\/strong><\/p><\/div><\/div><\/td>

Defination of Linear Transformation<\/strong><\/p>

<\/p><\/div><\/div><\/td>

Lecture 1<\/p>


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Lecture 1<\/p>


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Practical 1<\/p>


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Lecture 2<\/p>


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Lecture 2<\/span>
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Practical 2
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Lecture 3
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Lecture 3<\/span>
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Practical 3
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Lecture 4
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Lecture 4<\/span>
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Practical 4<\/p>


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Lecture 5
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Lecture 5<\/span>
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Practical 5<\/span>
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Lecture 6
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Lecture 6<\/span>
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Practical 6<\/span>
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Lecture 7
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Lecture 7<\/span>
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Practical 7
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Lecture 8
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Lecture 8<\/span>
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Practical 8<\/span>
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Lecture 9
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Lecture 9<\/span>
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Lecture 10
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Lecture 10<\/span>
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Lecture 11<\/span>
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Lecture 11<\/span>
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Lecture 12<\/span>
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Lecture 12<\/span>
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Lecture 13<\/span>
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Lecture 13<\/span><\/p>


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Lecture 14<\/span>
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Lecture 14<\/span>
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Lecture 15<\/span>
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Lecture 15<\/span>
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    Linear Algebra I<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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    Course Code: USMT302<\/p>

    Credits: 2 || Lecture\/week: 3
    Probable\/Actual Hrs Available: 45<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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    Unit I : System of Equations and Matrices<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    NAME OF UNIT<\/p><\/div><\/div><\/td>

    Titles \/ Details<\/p><\/div><\/div><\/td>

    Video Lectures<\/p><\/div><\/div><\/td>

    Lecture Notes<\/p><\/div><\/div><\/td>

    Assignments \/ Practicals<\/p><\/div><\/div><\/td>

    Ratings<\/p><\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Systems of homogeneous and non-homogeneous linear equations,<\/p><\/div><\/div><\/td>

    Lecture 1<\/p>


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    Lecture 1<\/p>


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    Practical 1<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
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    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Simple examples of finding solutions of such systems<\/p><\/div><\/div><\/td>

    Lecture 2<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 2<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Practical 2
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
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    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Geometric and algebraicunderstanding of the solutions.
    Matrices (with real entries),<\/p><\/div><\/div><\/td>

    Lecture 3
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 3<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Practical 3
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
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    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Matrix representation of system of homogeneous System <\/p><\/div><\/div><\/td>

    Lecture 4
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 4<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Practical 4<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
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    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Matrix representation of system of non-homogeneous System<\/p><\/div><\/div><\/td>

    Lecture 5
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 5<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Unit Test I<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Algebra of solutions of systems of homogeneous linear
    equations<\/p><\/div><\/div><\/td>

    Lecture 6
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 6<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    A system of homogeneous linear equations with number of unknowns more
    than the number of equations has infinitely many solutions.<\/p><\/div><\/div><\/td>

    Lecture 7
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 7<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
        0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Elementary row and column operations.<\/p><\/div><\/div><\/td>

    Lecture 8
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 8<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Row equivalent matrices. Row reduction (of a
    matrix to its row echelon form).<\/p><\/div><\/div><\/td>

    Lecture 9
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 9<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Gaussian elimination. Applications to solving systems of
    linear equations. Examples.<\/p><\/div><\/div><\/td>

    Lecture 10
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 10<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Elementary matrices. Relation of elementary row operations with elementary matrices.<\/p><\/div><\/div><\/td>

    Lecture 11<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 11<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Invertibility of elementary matrices.<\/p><\/div><\/div><\/td>

    Lecture 12<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 12<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Consequences such as (i) a square matrix is invertible
    if and only if its row echelon form is invertible<\/p><\/div><\/div><\/td>

    Lecture 13<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 13<\/span><\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    (ii) invertible matrices are products of
    elementary matrices.<\/p><\/div><\/div><\/td>

    Lecture 14<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 14<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    System of Equations and Matrices<\/p><\/div><\/div><\/td>

    Examples of the computation of the inverse of a matrix using Gauss
    elimination method<\/p><\/div><\/div><\/td>

    Lecture 15<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 15<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>