Let A= [ l 1 1 1 ] and B= [ ccc 9^ 2 & -10^ 2 & 11^ 2 12^ 2 & 13^… - Vidyadip

MCQ

Let $A=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2}\end{array}\right]$, then the value of $A ^{\prime} BA$ is.

A
$1224$
B
$1042$
C
$540$
✓
$539$

✓

Answer

Correct option: D.

$539$

d
$A ^{\prime} BA =\left[\begin{array}{lll}1 & 1 & 1\end{array}\right]\left[\begin{array}{lrc}9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2}\end{array}\right]\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$

$=\left[\begin{array}{lll}9^{2}+12^{2}-15^{2} & -10^{2}+13^{2}+16^{2} & 11^{2}-14^{2}+17^{2}\end{array}\right]$

$\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$

$=\left[9^{2}+12^{2}-15^{2}-10^{2}+13^{2}+16^{2}+11^{2}-14^{2}+17^{2}\right]$

$=[539]$

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