If A = [ 0 2 3 - 4 ] and k A = [ 0 3 a 2 b 24 ] , then the values of k , a , b are respectively:

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:

Smart Achievers · Accepted Answer

(3)

Ans. $- 6, - 4, - 9$

Explanation:

$k A = [\begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix}]$

$\Rightarrow$ $k [\begin{matrix} 0 & 2 \\ 3 & - 4 \end{matrix}] = [\begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix}]$

$\Rightarrow$ $[\begin{matrix} 0 & 2 k \\ 3 k & - 4 k \end{matrix}] = [\begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix}]$

$∴$ $- 4 k = 24$

$\Rightarrow$ $k = - 6$

$\Rightarrow$ $3 a = 2 \times (- 6)$

$\Rightarrow$ $3 a = - 12$

$\Rightarrow$ $a = - 4$

and $3 k = 2 b$

$\Rightarrow$ $3 \times (- 6) = 2 b$

$\Rightarrow$ $b = - 9$

Solution

Q.
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:

1 $- 6, - 12, - 18$

2 $- 6, 4, 9$

3 $- 6, - 4, - 9$

4 $- 6, 12, 18$

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Solution

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

1 -6, -12, -18

2 -6, 4, 9

3 -6, -4, -9

4 -6, 12, 18