Question

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'BA is

• A. 1224
• B. 1042
• C. 540
• D. 539

Answer 1

Answer: (D)

539

Answer 2

The correct answer is (D) : 539
Combining both the matrices we find,
$A'BA =$ $\begin{bmatrix} 1 & 1 & 1 \\\ \end{bmatrix}$ $=$ $\begin{bmatrix} 9^2 & -10^2 & 11^2 \\\ 12^2 & 13^2 & 14^2 \\\ -15^2 & 16^2 & 17^2 \\\ \end{bmatrix}$ $A$
$= [9^2+12^2 -15^2 -10^2 +13^2 +16^2 \ 11^2 -14^2 +17^ 2 ]$ $\begin{bmatrix} 1 \\\ 1 \\\ 1 \\\ \end{bmatrix}$
$= [(9^2 – 10^2) + (11^2 \+ 12^2) + (13^2 – 14^2) + (16^2 – 15^2) + 17^2]$
= [–19 + 265 + (–27) + 31 + 289]
= [585 – 46] = [539]