- #1
adc85
- 35
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I know how to find the determinant in general but these two problems here are tough for me:
1. Find the determinant of:
3 -1 0 0 0
-1 3 -1 0 0
0 -1 3 -1 0
0 0 -1 3 -1
0 0 0 -1 3
2. Find the determinant of:
0 2 2 2 2
2 0 2 2 2
2 2 0 2 2
2 2 2 0 2
2 2 2 2 0
Now, I know that I need to select a row or column that contains all zeros except for one number. The row or column that the one non-zero number is on would be selected as well. Then you would use the formula (for selecting row i and column j):
det A = (-1)^(i + j) * det A (without row i and column j)
But I can't figure out how to create a row or column full of zeros (except one element) for both of these problems. Thanks for any help.
1. Find the determinant of:
3 -1 0 0 0
-1 3 -1 0 0
0 -1 3 -1 0
0 0 -1 3 -1
0 0 0 -1 3
2. Find the determinant of:
0 2 2 2 2
2 0 2 2 2
2 2 0 2 2
2 2 2 0 2
2 2 2 2 0
Now, I know that I need to select a row or column that contains all zeros except for one number. The row or column that the one non-zero number is on would be selected as well. Then you would use the formula (for selecting row i and column j):
det A = (-1)^(i + j) * det A (without row i and column j)
But I can't figure out how to create a row or column full of zeros (except one element) for both of these problems. Thanks for any help.