First slide

Introduction to matrices

Question

If $A = (\begin{array}{cc} \cos â¡ Î± & â \sin â¡ Î± \\ \sin â¡ Î± & \cos â¡ Î± \end{array})$ and $A + A^{â²} = I$ , then $Î±$ equals

Easy

A

$2 n Ï Â\pm \frac{Ï}{2}, n â I$
B

$2 n Ï Â\pm \frac{Ï}{3}, n â I$
C

$2 n Ï Â\pm \frac{2 Ï}{3}, n â I$
D

$2 n Ï Â\pm \frac{4 Ï}{3}, n â I$

Solution

$\begin{array}{l} â [\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}] = [\begin{array}{cc} 2 \cos â¡ Î± & 0 \\ 0 & 2 \cos â¡ Î± \end{array}] \\ â 2 \cos â¡ Î± = 1 â \cos â¡ Î± = \frac{1}{2} = \cos â¡ \frac{Ï}{3} \\ â Î± = 2 n Ï Â\pm \frac{Ï}{3}, n â I \end{array}$

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