Without expanding the determinant, prove that SINGULAR MATRIX A square matrix A is said to be singular if |A| = 0. Also, A is called non singular if |A| ≠ 0.

Question

Philoid · Accepted Answer

We know that C₁⇒ C₁-C₂, would not change anything for the determinant.

Applying the same in above determinant, we get

Now it can clearly be seen that C₁=8 × C₃

Applying above equation we get,

We know that if a row or column of a determinant is 0. Then it is singular determinant.

Without expanding the determinant, prove that SINGULAR MATRIX A square matrix A is said to be singular if |A| = 0.Also, A is called non singular if |A| ≠ 0.

Without expanding the determinant, prove that
SINGULAR MATRIX A square matrix A is said to be singular if |A| = 0.

Also, A is called non singular if |A| ≠ 0.