If - - 1 2 0 3 -1 4 1 1 2 - the value of - 4 8 0 12 -4 16 4 4 8 - is

The correct option is C 64Δ Let A= | 4 8 0 12 4 16 4 4 8 | ∴ A= 4| 1 8 0 ...

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Standard XII

Mathematics

Properties of Determinants

If Δ =| 1 ...

Question

If $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 120 \end{matrix} \begin{matrix} 3 - 1 4 \end{matrix} \begin{matrix} 112 \end{matrix} ∣ ∣ ∣ ∣$ , the value of $∣ ∣ ∣ ∣ \begin{matrix} 480 \end{matrix} \begin{matrix} 12 - 4 16 \end{matrix} \begin{matrix} 448 \end{matrix} ∣ ∣ ∣ ∣$ is

12 Δ

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64 Δ

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4 Δ

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16 Δ

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Solution

The correct option is C $64 Δ$
Let $A =$ $∣ ∣ ∣ ∣ \begin{matrix} 480 \end{matrix} \begin{matrix} 12 - 4 16 \end{matrix} \begin{matrix} 448 \end{matrix} ∣ ∣ ∣ ∣$
$∴ A =$ $4 ∣ ∣ ∣ ∣ \begin{matrix} 180 \end{matrix} \begin{matrix} 3 - 4 16 \end{matrix} \begin{matrix} 148 \end{matrix} ∣ ∣ ∣ ∣$
$∴ A =$ $4 \times 4$ $∣ ∣ ∣ ∣ \begin{matrix} 120 \end{matrix} \begin{matrix} 3 - 1 16 \end{matrix} \begin{matrix} 118 \end{matrix} ∣ ∣ ∣ ∣$
$∴ A =$ $4 \times 4$ $\times 4$ $∣ ∣ ∣ ∣ \begin{matrix} 120 \end{matrix} \begin{matrix} 3 - 1 4 \end{matrix} \begin{matrix} 112 \end{matrix} ∣ ∣ ∣ ∣$
$∴ A =$ $64 Δ$

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Similar questions

Q. If the equation

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Question 126 (i)

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If Δ=∣∣ ∣∣1203−14112∣∣ ∣∣, the value of ∣∣ ∣∣48012−416448∣∣ ∣∣ is

The correct option is C 64ΔLet A=∣∣ ∣∣48012−416448∣∣ ∣∣∴A= 4∣∣ ∣∣1803−416148∣∣ ∣∣∴A= 4×4∣∣ ∣∣1203−116118∣∣ ∣∣∴A= 4×4×4∣∣ ∣∣1203−14112∣∣ ∣∣∴A= 64Δ

If $Δ = ∣ ∣ ∣ ∣ \begin{matrix} 120 \end{matrix} \begin{matrix} 3 - 1 4 \end{matrix} \begin{matrix} 112 \end{matrix} ∣ ∣ ∣ ∣$ , the value of $∣ ∣ ∣ ∣ \begin{matrix} 480 \end{matrix} \begin{matrix} 12 - 4 16 \end{matrix} \begin{matrix} 448 \end{matrix} ∣ ∣ ∣ ∣$ is