If A = diag1-12, B = diag23-1 and 3A + 4B = diagabc then the ascending order of a, b, c is

3A+4B=3000-30006+800012000-4 =1100090002 =diag 1192∴ asscending order is 2, 9, 11

If A = diag1-12, B = diag23-1 and 3A + 4B = diagabc then the ascending order of a, b, c is

3A+4B=3000-30006+800012000-4 =1100090002 =diag 1192∴ asscending order is 2, 9, 11

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If A $=$ diag $[\begin{matrix} 1 & - 1 & 2 \end{matrix}]$ , B $=$ diag $[\begin{matrix} 2 & 3 & - 1 \end{matrix}]$ and 3A $+$ 4B $=$ diag $[\begin{matrix} a & b & c \end{matrix}]$ then the ascending order of a, b, c is

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a, b, c

b, c, a

c, a, b

c, b, a

answer is D.

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Detailed Solution

$3 A + 4 B = [\begin{matrix} 3 & 0 & 0 \\ 0 & - 3 & 0 \\ 0 & 0 & 6 \end{matrix}] + [\begin{matrix} 8 & 0 & 0 \\ 0 & 12 & 0 \\ 0 & 0 & - 4 \end{matrix}] = [\begin{matrix} 11 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 2 \end{matrix}] = diag [\begin{matrix} 11 & 9 & 2 \end{matrix}]$