let-D-v-5-1-3-m-find-number-v-and-m-such-that-D-2-5I-I-identity-matrix-

Question Number 153227 by Eric002 last updated on 05/Sep/21

l e t D = [\begin{matrix} v 5 \\ \frac{1}{3} m \end{matrix}] f i n d n u m b e r (v) a n d

(m) s u c h t h a t D^{2} = 5 I (I = i d e n t i t y m a t r i x)

Answered by puissant last updated on 05/Sep/21

D^{2} = [\begin{matrix} v^{2} + \frac{5}{3} 5 v + 5 m \\ \frac{v}{3} + \frac{m}{3} \frac{5}{3} + m^{2} \end{matrix}] = [\begin{matrix} 5 0 \\ 0 5 \end{matrix}]

\Rightarrow {\begin{cases} v^{2} = 5 - \frac{5}{3} \\ v + m = 0 \end{cases}, {\begin{cases} v + m = 0 \\ m^{2} = 5 - \frac{5}{3} \end{cases}

\Rightarrow m = - v

v^{2} = \frac{10}{3} \Rightarrow v = \sqrt{\frac{10}{3}}; m = - \sqrt{\frac{10}{3}} . .

o r v = - \sqrt{\frac{10}{3}}; m = \sqrt{\frac{10}{3}} . .

Commented by Eric002 last updated on 05/Sep/21

w e l l d o n e

Answered by King1 last updated on 06/Sep/21

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