Q. 255.0( 1 Vote )

# The value of determinant

A. a^{3} + b^{3} + c^{3}

B. 3 bc

C. a^{3} + b^{3} + c^{3} – 3abc

D. none of these

Answer :

We have,

Applying C_{2}→ C_{2} + C_{3}, we get

Taking (a + b + c) common from second column, we get

Applying C_{1} → C_{1} – C_{3}, we get

Expanding along first row, we get

= (a + b + c)[(-b){c – b} – (1){-c^{2} – (-ab)} + a{-c – (-a)}]

= (a + b + c)(-bc + b^{2} + c^{2} – ab – ac + a^{2})

= a(-bc + b^{2} + c^{2} – ab – ac + a^{2}) + b(-bc + b^{2} + c^{2} – ab – ac + a^{2}) + c(-bc + b^{2} + c^{2} – ab – ac + a^{2})

= -abc + ab^{2} + ac^{2} – a^{2}b – a^{2}c + a^{3} – b^{2}c + b^{3} + bc^{2} – ab^{2} – abc + a^{2}b – bc^{2} + b^{2}c + c^{3} – abc – ac^{2} + a^{2}c

= a^{3} + b^{3} + c^{3} – 3abc

Hence, the correct option is (c)

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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