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Mathematics

If A = [354−2] and B =[24],\begin{bmatrix}[r] 3 & 5 \ 4 & -2 \end{bmatrix} \text{ and B } = \begin{bmatrix}[r] 2 \ 4 \end{bmatrix}, is the product AB possible? Give a reason. If yes find AB.

Matrices

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Answer

The product is possible because number of rows in A = number of columns in B =

AB=[354−2][24]=[3.2+5.44.2+(−2).4]=[260]AB = \begin{bmatrix}[r] 3 & 5 \ 4 & -2 \end{bmatrix} \begin{bmatrix}[r] 2 \ 4 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 3.2 + 5.4 \ 4.2 + (-2).4 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 26 \ 0 \end{bmatrix}

Hence, the matrix AB = [260].\begin{bmatrix}[r] 26 \ 0 \end{bmatrix}.

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