A^2 - 2A + 3I is:a.First row [8 7 -3], second row [1 13 7] and third row [2 17 22]b.First row [-1 7 -3], second row [0 1 -5] and third row [4 1 25]c.First row [8 1 0], second row [1 1 0] and third row [0 -7 22]d.First row [-7 5 -3], second row [1 18 15] and third row [-2 11 12]

Consider a 3x3 matrix denoted by A with first row [-1  3  2], second row [0  4  1] and third row [1  2  5], and another 3x3 matrix, B, with first row [6  2  -1], second row [3  5  2] and third row [-2  -3  0]. The matrix 2A-5B is:a.First row [-3 -2 -5], second row [-1 -1 -8] and third row [2 1 0]b.First row [2 -4 0], second row [5 7 -2] and third row [1 1 0]c.First row [-32 -4 9], second row [-15 -17 -8] and third row [12 19 10]d.First row [11 -3 5], second row [-1 6 -7] and third row [1 0 -2]

The matrix BA is:a.First row [0 7 -7], second row [1 4 7] and third row [2 -1 3]b.First row [-1 7 7], second row [10 17 8] and third row [2 -3 3]c.First row [-7 24 9], second row [-1 33 21] and third row [2 -18 -7]d.First row [-5 26 5], second row [-1 3 2] and third row [0 -18 -5]

The matrix AB is:a.First row [0 7 -7], second row [1 4 7] and third row [2 -1 3]b.First row [-1 7 7], second row [10 17 8] and third row [2 -3 3]c.First row [-1 0 1], second row [0 1 -8] and third row [-4 -3 3]d.First row [4 0 1], second row [1 1 8] and third row [2 -3 3]

(4 marks)Let A = (aij ) be the 4 × 4 matrix and D = (dij ) be the 4 × 1 matrix shown below.A =−3 1 1 01 1 2 −20 1 1 21 1 2 1 D =−1101(a) Evaluate4∑j=1a4j a2j

The matrix A transpose is:a.First row [-1 3 2], second row [0 4 1] and third row [1 2 5]b.First row [1 0 1], second row [0 1 0] and third row [0 0 1]c.First row [1 0 1], second row [0 -3 5] and third row [2 4 -5]d.First row [-1 0 1], second row [3 4 2] and third row [2 1