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    Matrices 1 PDF

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    1. The document provides examples of using elementary row operations to transform matrices. These include putting matrices in upper triangular form, finding inverses, and determining matrix rank. 2. Questions involve tasks like reducing matrices to unit matrices or upper triangular form, finding inverses, and determining matrix rank through row reduction. 3. Answers are provided for some examples, showing the step-by-step row operations used to transform the matrices as required.

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    Matrices 1 PDF

    Uploaded by

    ABC DEF
    39 views2 pages
    1. The document provides examples of using elementary row operations to transform matrices. These include putting matrices in upper triangular form, finding inverses, and determining matrix rank. 2. Questions involve tasks like reducing matrices to unit matrices or upper triangular form, finding inverses, and determining matrix rank through row reduction. 3. Answers are provided for some examples, showing the step-by-step row operations used to transform the matrices as required.

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    1. The document provides examples of using elementary row operations to transform matrices. These include putting matrices in upper triangular form, finding inverses, and determining matrix rank. 2. Questions involve tasks like reducing matrices to unit matrices or upper triangular form, finding inverses, and determining matrix rank through row reduction. 3. Answers are provided for some examples, showing the step-by-step row operations used to transform the matrices as required.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    39 views2 pages

    Matrices 1 PDF

    Uploaded by

    ABC DEF
    1. The document provides examples of using elementary row operations to transform matrices. These include putting matrices in upper triangular form, finding inverses, and determining matrix rank. 2. Questions involve tasks like reducing matrices to unit matrices or upper triangular form, finding inverses, and determining matrix rank through row reduction. 3. Answers are provided for some examples, showing the step-by-step row operations used to transform the matrices as required.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
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    Tutorial Sheet

    Course: B. Tech. Subject: Mathematics I

    Matrices

    1. What are singular and non singular matrices?


    1 3 3
    2. Transform 2 4 10 into a unit matrix by using elementary transformations.
    3 8 4
    1 2 2
    3. Reduce the matrix 1 2 1 to the upper triangular form by using elementary transformations.
    1 1 0

    1 2 2
    Ans: 0 4 1 [Answer may be different also].
    0 0 5

    4. Employing elementary transformations, find the inverse of the matrix


    1 2 3 1
    0 1 2
    1 3 3 2
    (i) 1 2 3 (ii) .
    2 4 3 3
    3 1 1
    1 1 1 1

    1 2 1 0
    1 1 1
    1 1 2 2 3
    Ans: (i) 8 6 2 (ii)
    2 0 1 1 1
    5 3 1
    2 3 2 3

    2 3 1 1
    1 1 2 4
    5. Find the rank of A if A= Ans: 3
    3 1 3 2
    6 3 0 7
    1 1 2
    6. For the matrix A = 1 2 3 , find non singular matrices P and Q such that PAQ is in normal form.
    0 1 1
    7. Reduce the following matrix to normal form and hence find its rank:
    1 2 1 4 1 2 1 3 1 3 2 5 1
    2 4 3 4 4 1 2 1 2 2 1 6 3
    (i) (ii) (iii)
    1 2 3 4 3 1 1 2 1 1 2 3 1
    1 2 6 7 1 2 0 1 0 2 5 2 3

    1
    2 1 3 6 1 2 3 2
    (iv) 3 3 1 2 (v) 2 3 5 1 Ans (i) 3 (ii) 3 (iii) 3 (iv) 3 (v) 2
    1 1 1 2 1 3 4 5

    0 0 0 0 0
    0 4 5 0 0
    8. Obtain a matrix N in the normal form equivalent to A= .Hence find non singular
    0 9 1 1 2
    0 10 0 1 11
    matrices P and Q such that PAQ=N.
    9. Find the inverse of the matrix M by applying elementary transformations:
    0 2 1 3 1 3 3 1
    1 1 1 2 1 1 1 0
    M= Ans: M 1 =
    1 2 0 1 2 5 2 3
    1 1 2 6 1 1 0 1

    10. Find the inverse of the following matrix by using row operations:

    3 3 4 1 1 0
    2 3 4 Ans: 2 3 4
    0 1 1 2 3 3

    1 1 2 3
    1 3 0 3
    11. Find the rank by reducing to normal form: Ans: 3
    1 2 3 3
    1 1 2 3

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