Question

Let A = $\begin{bmatrix} 0 & 2y & z \\ x & y & - z \\ x & - y & z \end{bmatrix}$ and A¢ . A = I, then the value of x² + y² + z² is –

• A. 1
• B. 2
• C. $\frac{1}{2}$
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

I = A¢A = $\begin{bmatrix} 0 & x & x \\ 2y & y & - y \\ z & - z & z \end{bmatrix}$ $\begin{bmatrix} 0 & 2y & z \\ x & y & - z \\ x & - y & z \end{bmatrix}$

= $\begin{bmatrix} 2x^{2} & 0 & 0 \\ 0 & 6y^{2} & 0 \\ 0 & 0 & 3z^{2} \end{bmatrix}$

\ 2x² = 6y² = 3z² = 1

\ x² + y² + z² = $\frac{1}{2} + \frac{1}{6} + \frac{1}{3} = \frac{3 + 1 + 2}{6} = 1$