Given-matrix-A-a-1-1-1-a-1-1-1-a-If-B-b-A-and-B-is-orthogonal-determine-value-of-a-and-b-

Question Number 115520 by bemath last updated on 26/Sep/20

G i v e n m a t r i x A = (\begin{matrix} a 1 1 \\ 1 a 1 \\ 1 1 a \end{matrix})

I f B = b . A a n d B i s o r t h o g o n a l

d e t e r m i n e v a l u e o f a a n d b .

Answered by bobhans last updated on 26/Sep/20

B = (\begin{matrix} a b b b \\ b a b b \\ b b a b \end{matrix}) \Rightarrow {(a b)}^{2} + b^{2} + b^{2} = 1

\Rightarrow a^{2} b^{2} + 2 b^{2} = 1; b^{2} (a^{2} + 2) = 1

\Rightarrow 2 {a b}^{2} + b^{2} = 0; b^{2} (2 a + 1) = 0

b = 0 \leftarrow r e j e c t e d; a = - \frac{1}{2}

b^{2} (\frac{1}{4} + 2) = 1 \Rightarrow b^{2} = \frac{1}{9 / 4} = \frac{4}{9}

b = \pm \frac{2}{3}

Commented by bemath last updated on 26/Sep/20

g r e a t t t

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