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Mathematics

Evaluate : if possible :

[32][20]\begin{bmatrix}[r] 3 & 2 \ \end{bmatrix}\begin{bmatrix}[r] 2 \ 0 \end{bmatrix}

Matrices

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Answer

[32][20]\begin{bmatrix}[r] 3 & 2 \ \end{bmatrix}\begin{bmatrix}[r] 2 \ 0 \end{bmatrix}

For matrix multiplication, the no. of columns in first matrix should be equal to no. of rows in the second matrix.

Hence, matrix multiplication is possible.

[32][20]=[3×2+2×0]=[6].\Rightarrow \begin{bmatrix}[r] 3 & 2 \ \end{bmatrix}\begin{bmatrix}[r] 2 \ 0 \end{bmatrix} = \begin{bmatrix}[r] 3 \times 2 + 2 \times 0 \ \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 6 \ \end{bmatrix}.

Hence, [32][20]=[6].\begin{bmatrix}[r] 3 & 2 \ \end{bmatrix}\begin{bmatrix}[r] 2 \ 0 \end{bmatrix} = \begin{bmatrix}[r] 6 \end{bmatrix}.

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