jee-main 2022 Q71

jee-main · India · session1_29jun_shift1 Matrices Matrix Power Computation and Application

Let $A = \left[ a _ { i j } \right]$ be a square matrix of order 3 such that $a _ { i j } = 2 ^ { j - i }$, for all $i , j = 1,2,3$. Then, the matrix $A ^ { 2 } + A ^ { 3 } + \ldots + A ^ { 10 }$ is equal to
(1) $\left( \frac { 3 ^ { 10 } - 1 } { 2 } \right) A$
(2) $\left( \frac { 3 ^ { 10 } + 1 } { 2 } \right) A$
(3) $\left( \frac { 3 ^ { 10 } + 3 } { 2 } \right) A$
(4) $\left( \frac { 3 ^ { 10 } - 3 } { 2 } \right) A$

Let $A = \left[ a _ { i j } \right]$ be a square matrix of order 3 such that $a _ { i j } = 2 ^ { j - i }$, for all $i , j = 1,2,3$. Then, the matrix $A ^ { 2 } + A ^ { 3 } + \ldots + A ^ { 10 }$ is equal to\\
(1) $\left( \frac { 3 ^ { 10 } - 1 } { 2 } \right) A$\\
(2) $\left( \frac { 3 ^ { 10 } + 1 } { 2 } \right) A$\\
(3) $\left( \frac { 3 ^ { 10 } + 3 } { 2 } \right) A$\\
(4) $\left( \frac { 3 ^ { 10 } - 3 } { 2 } \right) A$

Paper Questions

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