Answer :

Let

Given that Δ = 0.

We can write the determinant Δ as

Taking a, b and c common from C_{1}, C_{2} and C_{3}, we get

Recall that the value of a determinant remains same if we apply the operation R_{i}→ R_{i} + kR_{j} or C_{i}→ C_{i} + kC_{j}.

Applying C_{1}→ C_{1} + C_{2}, we get

Applying C_{1}→ C_{1} + C_{3}, we get

Taking common from C_{1}, we get

Applying R_{2}→ R_{2} – R_{1}, we get

Applying R_{3}→ R_{3} – R_{1}, we get

Expanding the determinant along C_{1}, we have

We have Δ = 0.

It is given that a, b and c are all non-zero.

Thus, when and a, b, c are all non-zero.

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Solve the matrix equations:

RD Sharma - Volume 1

Using properties of determinants, prove the following:

Mathematics - Board Papers

Using properties of determinants, prove the following:

Mathematics - Board Papers

Using properties of determinants, prove the following:

Mathematics - Board Papers

Solve the matrix equations:

RD Sharma - Volume 1