JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q64

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MathematicsSingle correct+4 / -1Question 64 of 90

If $A=\begin{bmatrix}5a&-b\\3&2\end{bmatrix}$ and $A\operatorname{adj}A=AA^T$ , then $5a+b$ is equal to :

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Answer and worked solution

Official answer: B

$A\operatorname{adj}A=|A|I$ with $|A|=10a+3b$ , and $AA^T=\begin{bmatrix}25a^2+b^2&15a-2b\\15a-2b&13\end{bmatrix}$ . So $15a=2b$ and $10a+3b=13$ , giving $a=\frac25$ , $b=3$ (and $25a^2+b^2=13$ checks). Then $5a+b=5$ .

Topics:Adjoint and inverse Matrix algebra

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 64