Suppcse Hha we desine the matri B-n +Ce2e eaer Arove that8 Assucias ae INn3 and SarzleSzC)...

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Question

Suppcse Hha we desine the matri B-n +Ce2e eaer Arove that8 Assucias ae INn3 and SarzleSzC) Itee

math Advanced-Math

Answer 1

Answer #1

Given that $В - 1n+ cjедei - сдезе$ and $Si(c) Inceie$ .

Let C S21 (2).S21 (-c1)

$(In + сдезей) (In — сдезей)$

$In -Ceecqezef - cj€ze3efege$ .

But $eje2 0$ , hence $C In-Cie2e ce3e$ .

To show $B C$ , we have to show $BC=CB=$

Look at $BC (InceeCege) (n-1e cege)$

Again using the fact that $e_i^t e_j = 0$ when $i \neq j$ , we get

$BC In ce2ec2e3ece2e-00 cee0 0 In$ .

Similarly $CB = I_n$ .

Therefore $B C$ .

Answer 2

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