Question

If possible, compute the matrix products using paper and pencil.

[101011112][123321213]\begin{bmatrix} 1 & 0 & -1\\0 & 1 & 1 \\ 1 & -1 & -2 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3\\ 3 & 2 & 1\\ 2 & 1 & 3 \end{bmatrix}

Solution

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Let us consider

A=[101011112]A=\begin{bmatrix} 1 &0 &-1\\ 0& 1 &1\\ 1 & -1&-2 \end{bmatrix}

and

B=[123321213]B=\begin{bmatrix} 1 &2& 3\\ 3 &2& 1\\ 2 &1& 3 \end{bmatrix}

. Clearly AA and BB are both 3×33\times 3 matrix and so number of columns in AA is equal to number of rows in BB. Thus matrix multiplication ABAB is defined.

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