Login

If A=diag[2,-5,9], B[-3,7,14] and C=Diag[4,-6,3],find (i) A+2B (II)B+C-A

$G i v e n, A = d i a g [2, - 5, 9], B = d i a g [- 3, 7, 14], a n d C = d i a g [4, - 6, 3] . T h e r e f o r e, A = [\begin{matrix} 2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9 \end{matrix}], B = [\begin{matrix} - 3 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 14 \end{matrix}], a n d C = [\begin{matrix} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & 3 \end{matrix}] (1) . A + 2 B = [\begin{matrix} 2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9 \end{matrix}] + 2 [\begin{matrix} - 3 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 14 \end{matrix}] \Rightarrow A + 2 B = [\begin{matrix} 2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9 \end{matrix}] + [\begin{matrix} - 6 & 0 & 0 \\ 0 & 14 & 0 \\ 0 & 0 & 28 \end{matrix}] \Rightarrow A + 2 B = [\begin{matrix} - 4 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 37 \end{matrix}] (2) . B + C - A = [\begin{matrix} - 3 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 14 \end{matrix}] + [\begin{matrix} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & 3 \end{matrix}] - [\begin{matrix} 2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9 \end{matrix}] \Rightarrow B + C - A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 17 \end{matrix}] - [\begin{matrix} 2 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 9 \end{matrix}] \Rightarrow B + C - A = [\begin{matrix} - 1 & 0 & 0 \\ 0 & 6 & 0 \\ 0 & 0 & 26 \end{matrix}]$

3

View Full Answer

Copyright © 2024 Aakash EduTech Pvt. Ltd. All rights reserved.

Aakash EduTech Pvt. Ltd.

What are you looking for?