InterviewSolution
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InterviewSolution
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If A = \(\begin{bmatrix}1 & 2 \\3 & -1 \\\end{bmatrix}\) and B = \(\begin{bmatrix}1 & 0 \\-1 & 0 \\\end{bmatrix},\) find |AB|. |
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Answer» Given that A = \(\begin{bmatrix} 1 & 2 \\ 3 & -1 \\ \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 0 \\ -1 & 0 \\ \end{bmatrix},\) we have to find |AB| Then, |A| = \(\begin{bmatrix} 1 & 2 \\ 3 & -1 \\ \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 0 \\ -1 & 0 \\ \end{bmatrix}\) |A| = 1 × -1 -2 × 3 = -7 (Expanding along R1) |B| = 1 × 0 - 0 × -1 = 0 (Expanding along R1) Since |AB| = |A||B|, Therefore |AB| = -7 × 0 = 0 |
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