if A=diag[2,-5,9], B=diag[-3,7,14] and c= diag[4,-6,3] find 2A+B-C - Maths - Matrices

Question

if A=diag[2,-5,9], B=diag[-3,7,14] and c= diag[4,-6,3] find
2A+B-C

Lalit Mehra · Accepted Answer

Given,

$A = diag [2, - 5, 9] = [\begin{matrix} 2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9 \end{matrix}] B = diag [- 3, 7, 14] = [\begin{matrix} - 3 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 14 \end{matrix}] C= diag [4, - 6, 3] = [\begin{matrix} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & 3 \end{matrix}] ∴ 2 A + B - C$

$= 2 [\begin{matrix} 2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9 \end{matrix}] + [\begin{matrix} - 3 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 14 \end{matrix}] - [\begin{matrix} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & 3 \end{matrix}] = [\begin{matrix} 4 & 0 & 0 \\ 0 & - 10 & 0 \\ 0 & 0 & 18 \end{matrix}] + [\begin{matrix} - 3 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 14 \end{matrix}] + [\begin{matrix} - 4 & 0 & 0 \\ 0 & 6 & 0 \\ 0 & 0 & - 3 \end{matrix}]$

$= [\begin{matrix} 4 - 3 - 4 & 0 & 0 \\ 0 & - 10 + 7 + 6 & 0 \\ 0 & 0 & 18 + 14 - 3 \end{matrix}] = [\begin{matrix} - 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 29 \end{matrix}] = diag [- 3, 3, 29]$

Thus, 2A + B – C = diag [ –3, 3, 29]

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