2. Let A be a matrix whose singular value decomposition is given by[0.40.4-0.4 -0.4 -0.4 0.6 [100 0 0 0-0.4 -0.4 0.6 -0.4 0 10 0 0A 0.4 -0.4 0.6 -0.4 -0.4 0 0 10 0-0.4 0 0 0 00.4 0 0 0 00.40.6 -0.40.4 0.4-0.40.40.60.5 0.5 0.5]-0.5 -0.5 0.50.50.5-0.5 -0.5 0.5 0.5-0.5 0.5 -0.5 0.5(a) Find A.(b) Determine rank of A.(c) Find eigenvalues of AT A.(d) Find the orthonormal basis for R(A).(e) Find the orthonormal basis for N(A).(f) Find the matrix B that is the closest matrix of rank 2 to A. Find the distance between A andB using the Frobenius norm.1

NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Let A be a matrix whose singular value decomposition is given by [0.4 -0.4 -0.4 -0.4 0.6 0.4 [100 000 -0.4 -0.4 0.6 -0.4 0 10 00 -0.4 0.6 -0.4 -0.4 0 0 10 0 0 0 0 A = 0.4 0.4 -0.4 0 0.6 -0.4 -0.4 0.4 0.6 0.4 0.4 0.4 0 0 0 0 (a) Find A. (b) Determine rank of A. (c) Find eigenvalues of AT A. 0.5 0.5 0.57 -0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 -0.5 0.5