The value of the determinant a b 0 0 a b b 0 a is equal to

The correct option is B a^3+b^3 a amp; b amp; 0 0 amp; a amp; b b amp; 0 amp; a =a( a ^ 2 0 ) b( 0 b ^ 2 ) +0= a ^ ...

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Byju's Answer

Standard XII

Mathematics

Definition of a Determinant

The value of ...

Question

The value of the determinant $∣ ∣ ∣ ∣ \begin{matrix} a & b & 0 0 & a & b b & 0 & a \end{matrix} ∣ ∣ ∣ ∣$ is equal to

a^{3} - b^{3}

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a^{3} + b^{3}

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none of these

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Solution

The correct option is B $a^{3} + b^{3}$
$∣ ∣ ∣ ∣ \begin{matrix} a & b & 0 0 & a & b b & 0 & a \end{matrix} ∣ ∣ ∣ ∣ = a (a^{2} - 0) - b (0 - b^{2}) + 0 = a^{3} + b^{3}$

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Similar questions

Q. The value of the determinant

|\begin{matrix} a - b & b + c & a \\ b - c & c + a & b \\ c - a & a + b & c \end{matrix}|

is

(a)

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

(b) 3bc
(c)

a^{3} + b^{3} + c^{3} - 3 a b c

(d) none of these

The value of $∣ ∣ ∣ ∣ \begin{matrix} a - b & b + c & a b - a & c + a & b c - a & a + b & c \end{matrix} ∣ ∣ ∣ ∣$

(a) $a^{3} + b^{3} + c^{3}$
(b) $3 b c$
(c) $a^{3} + b^{3} + c^{3} - 3 a b c$
(d) None of these

Which of the following is an expansion of the identity ${(a - b)}^{3}$ ?

a³ - b³ equals

The determinant $∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & a b & \frac{1}{a} + \frac{1}{b} 1 & b c & \frac{1}{b} + \frac{1}{c} 1 & c a & \frac{1}{c} + \frac{1}{a} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$ is equal to

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The value of the determinant ∣∣ ∣∣ab00abb0a∣∣ ∣∣ is equal to

The correct option is B a3+b3∣∣ ∣∣ab00abb0a∣∣ ∣∣=a(a2−0)−b(0−b2)+0=a3+b3

The value of the determinant $∣ ∣ ∣ ∣ \begin{matrix} a & b & 0 0 & a & b b & 0 & a \end{matrix} ∣ ∣ ∣ ∣$ is equal to

The correct option is B $a^{3} + b^{3}$
$∣ ∣ ∣ ∣ \begin{matrix} a & b & 0 0 & a & b b & 0 & a \end{matrix} ∣ ∣ ∣ ∣ = a (a^{2} - 0) - b (0 - b^{2}) + 0 = a^{3} + b^{3}$