Let $A=\begin{bmatrix}1 \\ 1 \\ 1\end{bmatrix}$ and $B=\begin{bmatrix}9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2}\end{bmatrix}$, then the value of $A^{\prime} BA$ is:

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Matrices

Let

A = 111

and

B = 9^{2} 1 2^{2} - 1 5^{2} - 1 0^{2} 1 3^{2} 1 6^{2} 1 1^{2} - 1 4^{2} 1 7^{2}

, then the value of

A^{'} B A

is:

Answer: (D)

A^{'} B A = [111] 9^{2} 1 2^{2} - 1 5^{2} - 1 0^{2} 1 3^{2} 1 6^{2} 1 1^{2} - 1 4^{2} 1 7^{2} 111

First multiply

A^{'} B

[9^{2} + 1 2^{2} - 1 5^{2} - 1 0^{2} + 1 3^{2} + 1 6^{2} 1 1^{2} - 1 4^{2} + 1 7^{2}]

Then multiply by

A

9^{2} + 1 2^{2} - 1 5^{2} - 1 0^{2} + 1 3^{2} + 1 6^{2} + 1 1^{2} - 1 4^{2} + 1 7^{2}

= 81 + 144 - 225 - 100 + 169 + 256 + 121 - 196 + 289 = 539

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Single correct option