Question

29. A matrix B is said to be a square root of a matrix A if BB A (a) Find two square roots of A = (b) How many different square roots can you find of - (c) Do you think that every 2 x 2 matrix has at least one square root? Explain your reasoning

Answer 1

a) given A = [2 2 2 2] Let a matrix B be a squarer root of A, so, B^2 = A Let B = [1 1 1 1] [1 1 1 1] [1 1 1 1] = [2 2 2 2] (= A) Hence, [1 1 1 1] is one of the roots of matrix A similarly , if B = [-1 -1 -1 -1] [-1 -1 -1 -1] [-1 -1 -1 -1] = [1 + 1 1 + 1 1 + 1 1 + 1] = [2 2 2 2] Hence, [-1 -1 -1 -1] is another root of matrix A so, Two squareroot s of [2 2 2 2] are [1 1 1 1] and [-1 -1 -1 -1] b) Given A = [5 0 0 9] Since A is a Diagonal matrix and the squarer roots of any Desired four squareroot s of A will be (1) [squareroot 5 0 0 3] (2) [-squareroot 5 0 0 3]