First slide

Operations of matrix

Question

If $A = [\begin{array}{ll} a b \\ b a \end{array}]$ and $A^{2} = [\begin{array}{ll} α β \\ β α \end{array}]$ , then

Easy

A

$α = a^{2} + b^{2}, β = 2 a b$
B

$α = a^{2} + b^{2}, β = a^{2} - b^{2}$
C

$α = 2 a b, β = a^{2} + b^{2}$
D

$α = a^{2} + b^{2}, β = - 2 a b$

Solution

$A^{2} = [\begin{array}{ll} a b \\ b a \end{array}] [\begin{array}{ll} a b \\ b a \end{array}] = [\begin{array}{cc} a^{2} + b^{2} & 2 a b \\ 2 a b & a^{2} + b^{2} \end{array}]$
$\begin{array}{ll} ∴ [\begin{array}{cc} α & β \\ β & α \end{array}] = [\begin{array}{cc} a^{2} + b^{2} & 2 a b \\ 2 a b & a^{2} + b^{2} \end{array}] \\ \Rightarrow α = a^{2} + b^{2}, β = 2 a b \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App