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Math Help - matrix equation

  1. #1
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    matrix equation

    completely stuck with this question

    Matrices A, B, C , D & X satisfy equation A(X + B)C = D, and D is a 5 5 matrix.
    i. If A has 3 columns, and C 4 rows, find the dimensions of each matrix.
    ii. Give conditions on the matrices A, B, C & D, if necessary, to ensure that we can solve the above equation. Find an expression for the unknown matrix


    Thanks
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  2. #2
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    Hello, Michael!

    Matrices A, B, C,D, X satisfy equation: . A(X + B)C \:=\:D .and D is a 55 matrix.

    (a) If A has 3 columns, and C has 4 rows, find the dimensions of each matrix.

    (b) Give conditions on the matrices A, B, C, D, if necessary,
    to ensure that we can solve the above equation.
    Find an expression for the unknown matrix

    We have: . \underbrace{A}_{(m\times3)} \underbrace{(X + B)}_{(r\times c)} \underbrace{C}_{(4\times n)} \:=\:\underbrace{D} _{(5\times5)}

    We see that: . m = 5,\;\;r\times c \:=\:3\times4,\;\;n = 5

    (a)Therefore: . A\!:5\times3,\;\;B\!:\;3\times4,\;\;C\!:4\times5

    (b) And X\!:\;3\times4
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