Is this inverse of a matrix correct C1 1 2 1 3 7 10 7 16 2

Is this inverse of a matrix correct ? C^-1 = [1 2 -1 3 7 -10 7 16 -21| 1 0 0 0 1 0 0 0 1] R\'_2 = R_2 - 3R_1 [1 2 -1 0 1 -7 7 16 -21| 1 0 0 -3 1 0 0 0 1] R\'_3= R_3 - 7R_1 [1 2 -1 0 1 -7 0 2 -14| 1 0 0 -3 1 0 -7 0 1] R\'_3 = R_3 - 2R_2 [1 2 -1 0 1 -7 0 0 0| 1 0 0 -3 1 0 -1 -2 1] No Solution/not possible.

Solution

yes, your solution is correct and precise.

This method is known as gauss jordan elimination method. In this method by using elementry row operations we try to convert A into I, simultaneously by performing same operations on I we get another matrix which gives us A^-1.

If any row\'s all elements in this process becomes zero, then for that matrix A^-1 is not possible.

In another words it means that deteminent of that matrix will be zero, that\'s why A^-1 doesn\'t exist.