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    Vector and Matrix Operations : Row Vectors, Column Vectors, Dot Product and Echelon Form

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    1. Find the dot product for the following pairs of vectors:
    a. Row vector = (2 0) Column vector is below
    5
    18
    b. Row vector = (3 9 -4) Column vector is below
    3
    0
    2
    c. Row vector = (5 6 7 8)
    1
    1
    1
    1

    The following matrices will be used in problems 2-3 below:
    0 -2 5
    A= 3 -4 17
    1 2 3
    9 7 2

    -3 3 0
    B= -4 -5 9
    -2 0 6
    -8 6 4

    3 3 0 -7
    X= 7 5 1 1
    4 3 3 -1

    4 1 0 5
    Y= 3 -2 7 1
    -5 8 -6 2
    2. Answer True or False using the matrices above

    a. 2A + 2B = 2(A + B)
    b. AT + BT = (A + B)T
    c. Let C = A * X, then C will be a 3 by 3 matrix
    d. Let D = Y * B, then D will be a 3 by 3 matrix
    e. (A * X)T = AT * BT

    3. Do the specified matrix multiplications. Show your work.

    a. A * X
    b. Y * B
    c. A * Y
    d. B * X

    4. Find the inverses of the following matrices
    a.
    8 6
    5 4
    b.
    3 2
    7 4
    c.
    8 5
    -7 -5
    d.
    3 -4
    7 -8

    5. Use elementary row operations to reduce the following matrices to echelon or reduced echelon form
    a.
    0 -2 -1
    3 0 0
    -1 1 1
    b.
    3 5 4
    1 0 1
    2 1 1
    c.
    3 6 7
    0 2 1
    2 3 4

    Please see the attached file for the fully formatted problems.

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    https://brainmass.com/math/linear-algebra/vector-and-matrix-operations-row-vectors-column-vectors-dot-product-and-echelon-form-52107

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    Vector and Matrix Operations, Row Vectors, Column Vectors, Dot Product and Echelon Form are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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