Let A = \[a ij] be a square matrix of order 3 such that a ij... | Mathematics | SolveeIt | Solveeit

Today, August 24

Question

Let A = [a ij] be a square matrix of order 3 such that a ij = 2 j – i , for all i , j = 1, 2, 3. Then, the matrix A 2 + A 3 + … + A 10 is equal to

A

$(\frac{3^{10}-3}{2})A$

B

$(\frac{3^{10}-1}{2})A$

C

$(\frac{3^{10}+1}{2})A$

D

$(\frac{3^{10}+3}{2})A$

Answer

$(\frac{3^{10}-3}{2})A$

Explanation

Solution

The correct option is(A): $(\frac{3^{10}-3}{2})A$

A 3 = A.A 2 = A(3 A) = 3 A 2 = 32 A

A 4 = 33 A

Now

A 2 + A 3 + … + A 10

A[31 + 32 + 33 + … + 39]

$(\frac{3^{10}-3}{2})A$