If A- 0 2- 3 -4 - and kA- 0 3a- 2b 24 - then the values of k- a- b are respectively-

Given, kA=[ 0 amp; 3a; 2b amp; 24 ]⇒ k [ 0 amp; 2; 3 amp; 4 ]=[ 0 amp; 3a; 2b amp; 24 ] ⇒ 2k=3a, 3k=2b, 4k=24 ⇒ a = 2k/3, b ...

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Byju's Answer

Standard XIII

Mathematics

Scalar Multiplication of a Matrix

If A=[ 0 2; 3...

Question

If $A = [\begin{matrix} 0 & 2 3 & - 4 \end{matrix}]$ and $k A = [\begin{matrix} 0 & 3 a 2 b & 24 \end{matrix}]$ , then the values of k, a, b are respectively.

-6, -12, -18

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-6, 4, 9

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-6, -4, -9

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-6, 12, 18

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Solution

The correct option is C -6, -4, -9
Given, $k A = [\begin{matrix} 0 & 3 a 2 b & 24 \end{matrix}] \Rightarrow k [\begin{matrix} 0 & 2 3 & - 4 \end{matrix}] = [\begin{matrix} 0 & 3 a 2 b & 24 \end{matrix}]$
$\Rightarrow 2 k = 3 a, 3 k = 2 b, - 4 k = 24$
$\Rightarrow a = \frac{2 k}{3}, b = \frac{3 k}{2}, k = - 6$
$\Rightarrow k = - 6, a = - 4, b = - 9$ .

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If A=[023−4] and kA=[03a2b24], then the values of k, a, b are respectively.

The correct option is C -6, -4, -9Given, kA=[03a2b24]⇒k[023−4]=[03a2b24] ⇒2k=3a,3k=2b,−4k=24 ⇒a=2k3,b=3k2,k=−6 ⇒k=−6,a=−4,b=−9.

If $A = [\begin{matrix} 0 & 2 3 & - 4 \end{matrix}]$ and $k A = [\begin{matrix} 0 & 3 a 2 b & 24 \end{matrix}]$ , then the values of k, a, b are respectively.