Engineering Board Exam Reviewer · Matrix Inverse and Cofactors · easy

A 2×2 matrix has determinant 0. Does it have an inverse?

1. No, it is singular
2. Yes, always
3. Only if it's symmetric
4. Yes, if all entries are positive

Answer

A. No, it is singular

Solution

A matrix with determinant 0 is singular and has no inverse.

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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?

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