If \(A = \begin{bmatrix} 1 & 2 & x \\ 3 & -1 & 2 \end{bmatrix}\) and \(B = \begin{bmatrix} y \\ x \\ 1 \end{bmatrix}\) be such that \(AB = \begin{bmatrix} 6 \\ 8 \end{bmatrix}\), then:
Show Hint
- \(y = 2x\)
- \(y = -2x\)
- \(y = x\)
- \(y = -x\)
The Correct Option is A
Solution and Explanation
So \(y + 3x = 6\) ... (i) and \(3y - x = 6\) ... (ii).
From (i), \(y = 6 - 3x\). Put in (ii): \(18 - 9x - x = 6\), so \(10x = 12\), \(x = \frac{6}{5}\), and \(y = 6 - \frac{18}{5} = \frac{12}{5}\).
Then \(y = \frac{12}{5} = 2 \cdot \frac{6}{5} = 2x\).
Answer: (1) \(y = 2x\)
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