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3 and 4 .Determinants and Matrices
easy
જો $A = \left[ {\begin{array}{*{20}{c}}0&1\\0&0\end{array}} \right], I$ એ $2$ કક્ષાનો એકમ શ્રેણિક છે અને $a, b$ એ સ્વૈર અચળાંક છે , તો ${(aI + bA)^2}$ = . . .
A
${a^2}I + abA$
B
${a^2}I + 2abA$
C
${a^2}I + {b^2}A$
D
એકપણ નહી.
Solution
(b) ${(aI + bA)^2} = \left[ {\begin{array}{*{20}{c}}a&b\\0&a\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}a&b\\0&a\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{a^2}}&{2ab}\\0&{{a^2}}\end{array}} \right] = {a^2}I + 2abA$.
Standard 12
Mathematics