Solve for DBC please Consider the matrices A, B, C, and D below.7-4-5244A =-75-2C =-5B =-7-3D =| 7-54-1-8-64-3 (6)DBC =

DBC=-5247-54-64-37-4-7-3-1-8-28-5-1 NOW…

Answered: 7 -4 -5 4 4 A = c- 5 -2 C = -5 8. B =|…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Solve for DBC please

Consider the matrices A, B, C, and D below.
7
-4
-5
2
4
4
A =
-7
5
-2
C =
-5
B =
-7
-3
D =| 7
-5
4
-1
-8
-6
4
-3

Expert Solution

Step 1

$D B C = [\begin{matrix} - 5 & 2 & 4 \\ 7 & - 5 & 4 \\ - 6 & 4 & - 3 \end{matrix}] [\begin{matrix} 7 & - 4 \\ - 7 & - 3 \\ - 1 & - 8 \end{matrix}] [\begin{matrix} - 2 & 8 \\ - 5 & - 1 \end{matrix}]$

NOW

$[\begin{matrix} 7 & - 4 \\ - 7 & - 3 \\ - 1 & - 8 \end{matrix}] [\begin{matrix} - 2 & 8 \\ - 5 & - 1 \end{matrix}] = [\begin{matrix} 7 \times (- 2) + (- 4) \times (- 5) & 7 \times (8) + (- 4) \times (- 1) \\ - 7 \times (- 2) + (- 3) \times (- 5) & - 7 \times (8) + (- 3) \times (- 1) \\ - 1 \times (- 2) + (- 8) \times (- 5) & - 1 \times (8) + (- 8) \times (- 1) \end{matrix}] = [\begin{matrix} - 14 + 20 & 56 + 4 \\ 14 + 15 & - 56 + 3 \\ 2 + 40 & - 8 + 8 \end{matrix}] = [\begin{matrix} 6 & 60 \\ 29 & - 53 \\ 42 & 0 \end{matrix}]$

HENCE

$[\begin{matrix} - 5 & 2 & 4 \\ 7 & - 5 & 4 \\ - 6 & 4 & - 3 \end{matrix}] [\begin{matrix} 7 & - 4 \\ - 7 & - 3 \\ - 1 & - 8 \end{matrix}] [\begin{matrix} - 2 & 8 \\ - 5 & - 1 \end{matrix}] = [\begin{matrix} - 5 & 2 & 4 \\ 7 & - 5 & 4 \\ - 6 & 4 & - 3 \end{matrix}] [\begin{matrix} 6 & 60 \\ 29 & - 53 \\ 42 & 0 \end{matrix}]$

NOW

$[\begin{matrix} - 5 & 2 & 4 \\ 7 & - 5 & 4 \\ - 6 & 4 & - 3 \end{matrix}] [\begin{matrix} 6 & 60 \\ 29 & - 53 \\ 42 & 0 \end{matrix}] = [\begin{matrix} - 5 \times 6 + 2 \times 29 + 4 \times 42 & - 5 \times 60 + 2 \times (- 53) + 4 \times 0 \\ 7 \times 6 - 5 \times 29 + 4 \times 42 & 7 \times 60 - 5 \times (- 53) + 4 \times 0 \\ - 6 \times 6 + 4 \times 29 - 3 \times 42 & - 6 \times 60 + 4 \times (- 53) - 3 \times 0 \end{matrix}] = [\begin{matrix} - 30 + 58 + 168 & - 300 - 106 + 0 \\ 42 - 145 + 168 & 420 + 265 + 0 \\ - 36 + 116 - 126 & - 360 - 212 + 0 \end{matrix}] = [\begin{matrix} 196 & - 406 \\ 65 & 685 \\ - 46 & - 572 \end{matrix}]$