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CBSE Class 12 · MatricesVery Short Answer

If

A = (cos α - sin α sin α cos α)

, find

α

satisfying

0 < α < \frac{π}{2}

when

A + A^{⊤} = 2 I_{2}

, where

A^{⊤}

is the transpose of

A

.

Answer: $α = \frac{π}{4}$

Solution

Add

A

to its transpose

A^{⊤} = (cos α sin α - sin α cos α)

; the off-diagonal terms cancel.

A + A^{⊤} = [2 cos α 0 0 2 cos α] = 2 I_{2} .

Hence

2 cos α = 2 \Rightarrow cos α = \frac{1}{2}

, and in

0 < α < \frac{π}{2}

this gives

α = \frac{π}{4}

.

α = \frac{π}{4}

CBSE Class 12 Board · Subjective

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