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Question: If $A = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ and $B = \begin{bmatrix} -5 & 4 & 0 \\ 0 & 2 & -1...

If A=[123]A = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} and B=[−54002−11−32]B = \begin{bmatrix} -5 & 4 & 0 \\ 0 & 2 & -1 \\ 1 & -3 & 2 \end{bmatrix}, then

A

AB=[−58004−23−96]AB = \begin{bmatrix} -5 & 8 & 0 \\ 0 & 4 & -2 \\ 3 & -9 & 6 \end{bmatrix}

B

AB=[−2 −1 4]AB = [-2 \ -1 \ 4]

C

AB=[−111]AB = \begin{bmatrix} -1 \\ 1 \\ 1 \end{bmatrix}

D

AB does not exist

Answer

AB does not exist

Explanation

Solution

Matrix A has dimensions 3×13 \times 1. Matrix B has dimensions 3×33 \times 3. For the matrix product ABAB to be defined, the number of columns in A must equal the number of rows in B. The number of columns in A is 1, and the number of rows in B is 3. Since 1≠31 \neq 3, the product ABAB is not defined.