3 and 4 .Determinants and Matrices
easy

यदि $A = \left[ {\begin{array}{*{20}{c}}a&b\\b&a\end{array}} \right]$ और ${A^2} = \left[ {\begin{array}{*{20}{c}}\alpha &\beta \\\beta &\alpha \end{array}} \right]$, तो

A

$\alpha = {a^2} + {b^2},\beta = ab$

B

$\alpha = {a^2} + {b^2},\beta = 2ab$

C

$\alpha = {a^2} + {b^2},\beta = {a^2} - {b^2}$

D

$\alpha = 2ab,\beta = {a^2} + {b^2}$

(AIEEE-2003)

Solution

(b) ${A^2} = \left[ {\begin{array}{*{20}{c}}\alpha &\beta \\\beta &\alpha \end{array}} \right] = \left[ {\begin{array}{*{20}{c}}a&b\\b&a\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}a&b\\b&a\end{array}} \right]$; $\alpha = {a^2} + {b^2};\,\beta = 2ab.$

Standard 12
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.