Q. 124.2( 27 Votes )

# Prove that where p is any scalar.

Answer :

Let Δ =

Applying Elementary Row Transformations

R_{2}→ R_{2} – R_{1} and R_{3}→ R_{3} – R_{1}

Δ =

Taking (y – x) and (z – x) common from R_{2} and R_{3} respectively

Δ = (y – x) (z – x)

Applying R_{3}→ R_{3} – R_{2}

Δ = (y – x) (z – x)

Taking (z – y) common from R_{3}

Δ = (y – x) (z – x) (z – y)

Expanding along R_{3}, we have

Δ = (x – y) (y – z) (z – x) [0 – 1 {x × p(y^{2} + x^{2} + xy) – 1 × (1 + px^{3})} + p (x + y + z) {x × (y + x) – 1 × x^{2}}

Δ = (x – y) (y – z) (z – x) (-px^{3} – pxy^{2} – px^{2}y + 1 + px^{3} + px^{2}y + pxy^{2} + pxyz)

Δ = (x – y) (y – z) (z – x) (1 + pxyz)

Hence, the given result is proved.

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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