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

Question

If k $\begin{bmatrix}

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

Answer 1

since A is orthogonal \ AA^T = I

̃k² $\left[ \begin{array} { c c c } - 1 & 2 & 2 \\ 2 & - 1 & 2 \\ 2 & 2 & - 1 \end{array} \right]$ $\begin{bmatrix}

̃ k² $\begin{bmatrix} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{bmatrix}$ = I

̃ 9k²I = I ̃ k = ± 1/3

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