Engineering Board Exam Reviewer · Matrix Inverse and Cofactors · easy

For A= bmatrix2&1\5&3 bmatrix (with (A)=1), what should A· A-1 equal?

1. bmatrix1&0\0&1 bmatrix
2. bmatrix2&1\5&3 bmatrix
3. bmatrix0&1\1&0 bmatrix
4. bmatrix1&1\1&1 bmatrix

Answer

A. bmatrix1&0\0&1 bmatrix

Solution

Any matrix times its inverse equals the identity matrix: bmatrix1&0\0&1 bmatrix.

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1. A 2×2 matrix has determinant 0. Does it have an inverse?
2. Find the inverse of A= bmatrix2&1\5&3 bmatrix.
3. Find the inverse of A= bmatrix4&7\2&6 bmatrix.
4. Find the cofactor C12 of the matrix bmatrix1&2&3\4&5&6\7&8&10 bmatrix.
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