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.

Algebra ->  Matrices-and-determiminant -> 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.      Log On


   

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) About Me  (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 AI. So append the 3x3 matrix %28matrix%283%2C3%2C1%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C1%29%29 to A=%28matrix%283%2C3%2C1%2C-2%2C-1%2C0%2C1%2C2%2C0%2C0%2C-1%29%29 to get







From there, just row reduce the 3x6 matrix to find A%5E%28-1%29. Let me know if you need help with the row reduction.


Note: you should get the answer: A%5E%28-1%29=%28matrix%283%2C3%2C1%2C2%2C3%2C0%2C1%2C2%2C0%2C0%2C-1%29%29