Matrix Inverse and Cofactors — Engineering Board Exam Practice Questions

10 free engineering board exam reviewer questions on Matrix Inverse and Cofactors (Advanced Engineering Mathematics), each with the correct answer and a worked solution.

1. Find the inverse of A= bmatrix2&1\5&3 bmatrix.
2. Find the inverse of A= bmatrix4&7\2&6 bmatrix.
3. Find the cofactor C12 of the matrix bmatrix1&2&3\4&5&6\7&8&10 bmatrix.
4. For the matrix A= bmatrix3&2\1&4 bmatrix, find the cofactor matrix.
5. For A= bmatrix2&1\5&3 bmatrix (with (A)=1), what should A· A-1 equal?
6. A 2×2 matrix has determinant 0. Does it have an inverse?
7. Find the sum of all entries of A-1 if A= bmatrix2&1&0\1&2&1\0&1&2 bmatrix.
8. Find the (1,2) entry of A-1 if A= bmatrix1&2&1\0&1&3\2&1&0 bmatrix.
9. Find the cofactor C23 of A= bmatrix2&1&3\0&4&-1\5&2&6 bmatrix.
10. Find the inverse of A= bmatrix5&2\4&3 bmatrix.