1. 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

2. Hello, Michael!

Matrices $A, B, C,D, X$ satisfy equation: . $A(X + B)C \:=\:D$ .and $D$ is a 5×5 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 $X\!:\;3\times4$