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 and Answers Forum

All Questions Topic List
Matrices and Determinants Questions
Previous in All Question Next in All Question
Previous in Matrices and Determinants Next in Matrices and Determinants
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

	$g r e a t t t$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum