If A = 023-4 and k A = 03a2b24 then find the value of b-a -k

Solution:

We have, $A = [\begin{matrix} 0 & 2 \\ 3 & - 4 \end{matrix}] \Rightarrow k A = [\begin{matrix} 0 & 2 k \\ 3 k & - 4 k \end{matrix}]$

But $k A = [\begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix}] ∴ [\begin{matrix} 0 & 2 k \\ 3 k & - 4 k \end{matrix}] = [\begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix}] \Rightarrow 2 k = 3 a, 3 k = 2 b, - 4 k = 24 \Rightarrow k = - 6, a = - 4, b = - 9$

Hence, $b - a - k = - 9 - (- 4) - (- 6) = - 9 + 4 + 6 = 1$

If $A = [\begin{matrix} 0 & 2 \\ 3 & - 4 \end{matrix}]$ and $k A = [\begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix}]$ then find the value of $b - a - k$

Solution:

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