Question

Find all possible matrix products of two different matrices among the three
matrices below.

A = -1, 3, 4
0, -2, 5

B= -2, 4, 3
-1, -4, 2
2, 4, 3

C= -3, 2
-1, 6

Answer 1

Answer on Question #56710 – Math – Linear Algebra

Find all possible matrix products of two different matrices among the three matrices below.

A = -1, 3, 4

0, -2, 5

B = -2, 4, 3

-1, -4, 2

2, 4, 3

C = -3, 2

-1, 6

Solution

Given

$$A = \begin{pmatrix} -1 & 3 & 4 \\ 0 & -2 & 5 \end{pmatrix}, \quad B = \begin{pmatrix} -2 & 4 & 3 \\ -1 & -4 & 2 \\ 2 & 4 & 3 \end{pmatrix}, \quad C = \begin{pmatrix} -3 & 2 \\ -1 & 6 \end{pmatrix},$$

calculate

$$AB = \begin{pmatrix} 7 & -8 & 15 \\ 12 & 28 & 11 \end{pmatrix}$$ $$CA = \begin{pmatrix} 3 & -13 & -2 \\ 1 & -15 & 5 \end{pmatrix}$$

Other products do not exist.

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