SOLUTION: Let A = 1 -2 -1 0 1 2 0 0 -1 A. Calculate the determinant of A. Does the inverse matrix exist? If so, then calculate Ainverse.

Question 191470: Let A =
1 -2 -1
0 1 2
0 0 -1
A. Calculate the determinant of A.
Does the inverse matrix exist? If so, then calculate Ainverse.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since we have a upper triangular matrix, this means that the determinant is simply the product of all of the diagonal entries. So

det(A)=(1)(1)(-1)=-1

So the determinant of A is -1

Since the determinant is NOT equal to zero, this means that the inverse of A exists. To find the inverse of A, you have many options, but the best option (in my opinion) is to row reduce the augmented matrix . So append the 3x3 matrix to to get

From there, just row reduce the 3x6 matrix to find . Let me know if you need help with the row reduction.

Note: you should get the answer:
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