Mathematics 2001 JAMB Past Questions - Question 18: Given the matrix K=(2 1 ,3 4) ,the matrix K² +K+1 ,where I is the 2x2 identify matrix is

Correct Answer

B

Explanation

To find the matrix K² + K + 1, we first need to calculate the square of matrix K.Matrix K:K = [2 1]    [3 4]Square of matrix K (K²):K² = K * KK * K = [2 1] * [2 1]          [3 4] [3 4]Calculating the matrix multiplication:K * K = [(2*2 + 1*3) (2*1 + 1*4)]          [(3*2 + 4*3) (3*1 + 4*4)]K * K = [7 6]          [18 19]Now, let's add K² to K and then add the identity matrix:K² + K = [7 6] + [2 1]            [18 19] [3 4]Adding the matrices:K² + K = [7+2 6+1]            [18+3 19+4]K² + K = [9 7]            [21 23]Finally, let's add 1 to the resulting matrix:K² + K + 1 = [9+1 7+1]                  [21+1 23+1]K² + K + 1 = [10 8]                  [22 24]Therefore, the matrix K² + K + 1, where K is the given matrix, and I is the 2x2 identity matrix, is:[10 8][22 24]