Question

If 3A = $\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{bmatrix}$and A. A^t = I, then x + y equal to

• A. –1
• B. 1
• C. 2
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

AA^–1= $\frac { 1 } { 9 }$ $\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{bmatrix}$

$\begin{bmatrix} 1 & 2 & x \\ 2 & 1 & 2 \\ 2 & - 2 & y \end{bmatrix}$= $\frac { 1 } { 9 }$ $\begin{bmatrix} 9 & 0 & x + 4 + 2y \\ 0 & 9 & 2x + 2 - 2y \\ x + 4 + 2y & 2x + 2 - 2y & x^{2} + 4 + y^{2} \end{bmatrix}$

I = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

Ž x = –2, y = –1

Ž x + y = – 3