6. Use Gaussian elimination to find the determinant of the matrix 1 3 2 4 1648...

   

Transcribed Image Text:

6. Use Gaussian elimination to find the determinant of the matrix 1 3 2 4 1648 A = 1300 2 64 12, 7. Find the determinant of the linear transformation T(S)=2f+3f' from P to P. Recall that P (a+b+cr: a, b, c are real numbers}. 8. If A is an invertible n x n matrix and v is an eigenvector of A with eigenvalue A, (a) Is van eigenvector of A3? If so, what is its eigenvalue? (b) Is v an eigenvector of A-1? If so, what is its eigenvalue? (c) Is van eigenvector of A + 21,? If so, what is its eigenvalue? 1 6. Use Gaussian elimination to find the determinant of the matrix 1 3 2 4 1648 A = 1300 2 64 12, 7. Find the determinant of the linear transformation T(S)=2f+3f' from P to P. Recall that P (a+b+cr: a, b, c are real numbers}. 8. If A is an invertible n x n matrix and v is an eigenvector of A with eigenvalue A, (a) Is van eigenvector of A3? If so, what is its eigenvalue? (b) Is v an eigenvector of A-1? If so, what is its eigenvalue? (c) Is van eigenvector of A + 21,? If so, what is its eigenvalue? 1