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Thread: 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 $\displaystyle A, B, C,D, X$ satisfy equation: .$\displaystyle A(X + B)C \:=\:D$ .and $\displaystyle D$ 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 $\displaystyle A, B, C, D$, if necessary,
    to ensure that we can solve the above equation.
    Find an expression for the unknown matrix

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

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

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

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