Let A = a i j 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 + … + A 10 is equal to

Question

Let A = a i j be a square matrix of order 3 such that a i j = 2 j - i , for all i , &#160; j = 1 , 2 , 3 . Then, the matrix A 2 + A 3 + &#8230; + A 10 is equal to

Aicharya · Accepted Answer

Given, A = a i j 3 &#215; 3 where a i j = 2 j - i we get, A = 1 2 4 1 2 1 2 1 4 1 2 1 A 2 = 1 2 4 1 2 1 2 1 4 1 2 1 1 2 4 1 2 1 2 1 4 1 2 1 &#8658; A 2 = 3 6 12 3 2 3 6 3 4 3 2 3 = 3 A &#8658; A 3 = 3 A 2 = 9 A Now, A 2 + A 3 + A 4 + &#8943; A 10 = 3 A + 3 2 A + 3 3 A + &#8943; 3 9 A = 3 A 3 9 - 1 3 - 1 = A 3 10 - 3 2

Let A = a i j be a square matrix of order 3 such that a i j = 2 j - i , for all i ,   j = 1 , 2 , 3 .…

Solution

Let A = a i j be a square matrix of order 3 such that a i j = 2 j - i , for all i , &#160; j = 1 , 2 , 3 .…

Solution

Let A = a i j be a square matrix of order 3 such that a i j = 2 j - i , for all i , j = 1 , 2 , 3 .…