3. If a 4x 4 matrix A has eigenvalues 1,-1, 2 and -2, then answer the...

 

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3. If a 4x 4 matrix A has eigenvalues 1,-1, 2 and -2, then answer the following questions. (a) Compute the determinant of A. (b) Compute the determinant of AAT. (c) Compute the trace of A. (d) Compute the eigenvalues of A. (e) Compute the eigenvalues of A +31. (f) Is A invertible? If so, compute its eignevalues A-. (g) Compute the eigenvalues of A-3 (h) Compute the eigenvalues of (A+27)- -[2])--[9) ---=[ ] B= and C= (4 points) Lef A = Compute the following matrices if possible. If the operation is not possible, enter DNE. (a) Compute-3A [[6,-21],[-6,9]] (b) Compute 2A +3B [[-13,22] [16,6]] (c) Compute 5B-4C IDE (d) Compute AC IDE (e) Compute CA (f) Compute AB (9) Compute A2. [1-4,49),(4,-9]] (h) Compute C [1,64] [9,0] [25.-1]] 3. If a 4x 4 matrix A has eigenvalues 1,-1, 2 and -2, then answer the following questions. (a) Compute the determinant of A. (b) Compute the determinant of AAT. (c) Compute the trace of A. (d) Compute the eigenvalues of A. (e) Compute the eigenvalues of A +31. (f) Is A invertible? If so, compute its eignevalues A-. (g) Compute the eigenvalues of A-3 (h) Compute the eigenvalues of (A+27)- -[2])--[9) ---=[ ] B= and C= (4 points) Lef A = Compute the following matrices if possible. If the operation is not possible, enter DNE. (a) Compute-3A [[6,-21],[-6,9]] (b) Compute 2A +3B [[-13,22] [16,6]] (c) Compute 5B-4C IDE (d) Compute AC IDE (e) Compute CA (f) Compute AB (9) Compute A2. [1-4,49),(4,-9]] (h) Compute C [1,64] [9,0] [25.-1]]