Find a singular value decomposition of the matrix A = 21 12 -2 2 40 Use part (a) to find a singular value decompostion of the matrix AT =[ = 21-24 12 20

Find the rank and the nullity of the matrix rank (A) = nullity (A) = = rank(A) + nullity (A) = choose > A = -1 -2 -1 -2 -1 3 0 -1 -2 -1 2-5 TT 3 -8

|X= 3 -2 -2 2 ဦး + 0 1 + --L 1 Find a Basis for Column B of this Matrix

Prove that the sum of two negative definite matrices A and B is negative definite (A+B) meaning that for matrix (A+B) all eigen values will be negative or have negative real parts