Question

Use elementary row operations to find det(A) where A=. 1 1 -3 8

0 1 1 -2
| 2 0 1 1 |
0 1 0 1

Answer 1

To find det(A) using elementary row operations, we need to perform a series of operations to transform matrix A into row-echelon form or reduced row-echelon form.

Step-by-step explanation:

To find det(A) using elementary row operations, we need to perform a series of operations to transform matrix A into row-echelon form or reduced row-echelon form. Let's denote the given matrix as A:

A = [1 1 -3 8 | 2 ; 0 1 1 -2 | 0 ; 1 0 1 1 | 0 ; 1 1 1 1 | 1]

1. Start with the first row and subtract Row 1 from Row 2, Row 3, and Row 4:
2. [1 1 -3 8 | 2 ;
3. 0 1 1 -2 -0 | -2
4. ;
5. 1 0 1 1 - 0 | - 2
6. ;
7. 1 1 1 1 - 1 | - 1
8. ]
9. Next, subtract Row 1 from Row 3 and Row 4:
10. [1 1 -3 8 | 2 ; 0 1 1 -2 | -2 ;
11. 1 0 1 1 - 1 | - 3
12. ;
13. 1 1 1 1 - 1 | - 1
14. ]
15. Now, subtract Row 2 from Row 4:
16. [1 1 -3 8 | 2 ; 0 1 1 -2 | -2 ; 1 0 1 1 | - 3 ;
17. 1 0 0 0 - 0 | 1
18. ]

The resulting matrix is now in row-echelon form. The determinant of a triangular matrix is the product of the diagonal elements, so we have:

det(A) = 1 x 1 x 1 = 1