MathematicsIf A=0−124,kA=abcdthen the ascending order of a,b,c is

If $A = [\begin{matrix} 0 & - 1 \\ 2 & 4 \end{matrix}], k A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ then the ascending order of a,b,c is

A
a, b, c
B
c, b, a
C
a, c, b
D
c, a, b

Solution:

$A = [\begin{matrix} 0 & - 1 \\ 2 & 4 \end{matrix}]$

$\begin{array}{l} k A = k [\begin{matrix} 0 & - 1 \\ 2 & 4 \end{matrix}] = [\begin{matrix} 0 & - k \\ 2 k & 4 k \end{matrix}] = [\begin{matrix} a & b \\ - 8 & c \end{matrix}] \\ \Rightarrow a = 0, b = - k, 2 k = - 8 \\ \Rightarrow k = - 4 \\ c = 4 k \\ a = 0, b = 4 c = - 16 \end{array}$

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