Question

1. Construct a random integer-valued 4x4 matrix A. 2. Use Excel and the function MDETERM to calculate the determinant of A. If A is not invertible, choose another A. 3. Reduce A to echelon form U with no row scaling. 4. Use the formula det A = {(-1)^r (product of the pivots in U) when A is invertible / 0 when A is not invertible Where r is the number of row exchanges to calculate the determinant of A. 5. Compute the eigenvalues of A and the product of these eigenvalues (as accurately as possible). 6. List the matrix A, and to 4 decimal places, list the pivots in U and the eigenvalues of A. Compare the determinant of A with the products you found above.

          1. Construct a random integer-valued 4x4 matrix A.

2. Use Excel and the function MDETERM to calculate the determinant of A. If A is not invertible,
choose another A.

3. Reduce A to echelon form U with no row scaling.

4. Use the formula det A = {(-1)^r (product of the pivots in U) when A is invertible / 0 when A is not invertible

Where r is the number of row exchanges to calculate the determinant of A.

5. Compute the eigenvalues of A and the product of these eigenvalues (as accurately as
possible).

6. List the matrix A, and to 4 decimal places, list the pivots in U and the eigenvalues of A.
Compare the determinant of A with the products you found above.

1. Construct a random integer-valued 4x4 matrix A.

2. Use Excel and the function MDETERM to calculate the determinant of A. If A is not invertible,
choose another A.

3. Reduce A to echelon form U with no row scaling.

4. Use the formula det A = (-1)^r (product of the pivots in U) when A is invertible / 0 when A is not invertible

Where r is the number of row exchanges to calculate the determinant of A.

5. Compute the eigenvalues of A and the product of these eigenvalues (as accurately as
possible).

6. List the matrix A, and to 4 decimal places, list the pivots in U and the eigenvalues of A.
Compare the determinant of A with the products you found above.

Added by Vicenta T.

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