- K88 x-lend vmatrix is not equal toA- beginvmatrix 2 - 1 - 1 2 - 2 - 3 2 - 3 - 6lend vmatrix 2 - 1 - 1 N3 - 2 - 3 83 - 6lend vmatrix 3 - 1 - 1 6 - 2 - 3 11083 - 6vmatrix D- begin vmatrix 1 - 2 - 11118583 1 - 9 - 6vmatrix

The correct option is A 2 amp; 1 amp; 1 2 amp; 2 amp; 3 2 amp; 3 amp; 61 amp; 1 amp; 1 1 amp; 2 amp; 3 1 amp; 3 amp;6 = ...

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Byju's Answer

Standard XII

Mathematics

Evaluation of a Determinant

&& K88 x&&len...

Question

The determinant $ $∣ ∣ ∣ ∣ \begin{matrix} \end{matrix} ∣ ∣ ∣ ∣$ $ is not equal to

∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 2 & 2 & 3 2 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣

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∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 3 & 2 & 3 4 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣

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∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 1 1 & 5 & 3 1 & 9 & 6 \end{matrix} ∣ ∣ ∣ ∣

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∣ ∣ ∣ ∣ \begin{matrix} 3 & 1 & 1 6 & 2 & 3 10 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣

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Solution

The correct option is A $∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 2 & 2 & 3 2 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & 2 & 3 1 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 3 & 2 & 3 4 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣ b y C_{1} \to C_{1} + C_{2} ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 1 1 & 5 & 3 1 & 9 & 6 \end{matrix} ∣ ∣ ∣ ∣ b y C_{2} \to C_{2} + C_{3} ∣ ∣ ∣ ∣ \begin{matrix} 3 & 1 & 1 6 & 2 & 3 10 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣, b y C_{1} \to C_{1} + C_{2} + C_{3} . B u t \neq ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 2 & 2 & 3 2 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣$ .

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Similar questions

Q. The determinant

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & 2 & 3 1 & 3 & 6 \end{matrix} ∣ ∣ ∣ ∣

is not equal to

Q. If

∣ ∣ ∣ \begin{matrix} 3 & x x & 1 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 3 & 2 4 & 1 \end{matrix} ∣ ∣ ∣

then

x

is equal to

Evaluate the determinants..

$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 4 & 5 1 & 1 & - 2 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 & 2 - 1 & 0 & - 3 - 2 & 3 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & - 2 0 & 2 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

If $∣ ∣ ∣ \begin{matrix} x & 2 18 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & 2 18 & 6 \end{matrix} ∣ ∣ ∣$ , then x is equal to
a) 6
b) $\pm 6$
c) -6
d) zero

Q. Evaluate the determinants
(i)

∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & - 0 \end{matrix} ∣ ∣ ∣ ∣

(ii)

∣ ∣ ∣ ∣ \begin{matrix} 3 & - 4 & 5 1 & 1 & - 2 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣

(iii)

∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 & 2 - 1 & 0 & - 3 - 2 & 3 & 0 \end{matrix} ∣ ∣ ∣ ∣

(iv)

∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & - 2 0 & 2 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣

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The determinant \(∣∣ ∣∣∣∣ ∣∣\) is not equal to

The correct option is A ∣∣ ∣∣211223236∣∣ ∣∣∣∣ ∣∣111123136∣∣ ∣∣=∣∣ ∣∣211323436∣∣ ∣∣ by C1→C1+C2∣∣ ∣∣121153196∣∣ ∣∣ by C2→C2+C3∣∣ ∣∣3116231036∣∣ ∣∣, by C1→C1+C2+C3.But ≠∣∣ ∣∣211223236∣∣ ∣∣.

The determinant \( $∣ ∣ ∣ ∣ \begin{matrix} \end{matrix} ∣ ∣ ∣ ∣$ \) is not equal to