Show that matrix multiplication distributes over matrix addition. That is, show that A(B+C) = AB + AC for any matrices A, B, and C of compatible size.
Added by Amy M.
Step 1
Step 1:** Let matrices A, B, and C be defined as follows: \[ A = \begin{bmatrix} 2005 \end{bmatrix} \] \[ B = \begin{bmatrix} 5010 \end{bmatrix} \] \[ C = \begin{bmatrix} 1001 \end{bmatrix} \] ** Show more…
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In this exercise we show that matrix multiplication is dis- tributive over matrix addition. a) Suppose that $A$ and $B$ are $m \times k$ matrices and that $C$ is a $k \times n$ matrix. Show that $(A+B) C=A C+B C$ . b) Suppose that $C$ is an $m \times k$ matrix and that $A$ and $B$ are $k \times n$ matrices. Show that $C(A+B)=C A+C B$
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