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Mathematics

If matrix A = [−12]\begin{bmatrix}[r] -1 & 2 \end{bmatrix} and matrix B = [34]\begin{bmatrix}[r] 3 \ 4 \end{bmatrix}, then matrix AB is equal to:

1.[−3]1. \begin{bmatrix}[r] -3 \end{bmatrix}

2.[8]2. \begin{bmatrix}[r] 8 \end{bmatrix}

3.[5]3. \begin{bmatrix}[r] 5 \end{bmatrix}

4.[−1234]4. \begin{bmatrix}[r] -1 & 2 \ 3 & 4 \end{bmatrix}

Matrices

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Answer

Calculating,

⇒AB=[−12][34]=[−1×3+2×4]=[−3+8]=[5].\Rightarrow AB = \begin{bmatrix}[r] -1 & 2 \ \end{bmatrix}\begin{bmatrix}[r] 3 \ 4 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] -1 \times 3 + 2 \times 4 \ \end{bmatrix} \\[1em] = \begin{bmatrix}[r] -3 + 8 \ \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 5 \end{bmatrix}.

Hence, option 3 is the correct option.

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