Fill in with the missing integers given that each of the matrices below is diagonalizable. (a) If A is a diagonalizable 4 by 4 matrix and its characteristic polynomial is X* (A – 1)(A+3), then Null(A) = (b) If B is a diagonalizable 5 by 5 matrix with eigenvalues -1, 1, 2 then dim(Null(B – 21)) = (c) If C is a diagonalizable 8 by 8 matrix with eigenvalues -4, 0, 5, 9, then pivot columns. (d) If D is a diagonalizable 6 by 6 matrix whose rank is 2 and its characteristic polynomial is 1*(A – 1)'(A + 3)™, then where k= |= and m=

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