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Question: If k . \(\begin{bmatrix} - 1 & 2 & 2 \\ 2 & - 1 & 2 \\ 2 & 2 & - 1 \end{bmatrix}\)is an orthogonal ...

If k . $\begin{bmatrix}

  • 1 & 2 & 2 \ 2 & - 1 & 2 \ 2 & 2 & - 1 \end{bmatrix}$is an orthogonal matrix, then k is equal

to-

A

1

B

½

C

1/3

D

None of these

Answer

1/3

Explanation

Solution

Let A = k $\begin{bmatrix}

  • 1 & 2 & 2 \ 2 & - 1 & 2 \ 2 & 2 & - 1 \end{bmatrix}$

Since A is orthogonal \ AAT = I

k2 [900090009]\begin{bmatrix} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{bmatrix}= IŽ 9k2I = I Ž k2 = 19\frac{1}{9}Ž k = ± 13\frac{1}{3}