JEE Main 2014 · 12 Apr · Shift 1 · Mathematics Q65

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MathematicsSingle correct+4 / -1Question 65 of 90

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 :

y=2x

y=-2x

y=x

y=-x

Answer and worked solution

Official answer: A

$AB=\begin{bmatrix}y+3x\\3y-x+2\end{bmatrix}=\begin{bmatrix}6\\8\end{bmatrix}$ . So $y+3x=6$ and $3y-x=6$ , giving $x=\frac65$ , $y=\frac{12}5$ . Hence $y=2x$ .

Topics:Matrix algebra

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JEE Main 2014 · 12 Apr · Shift 1, Mathematics question 65