8. Express the following linear systems (from) in the form of matrix equations. { (a). (b). 21 2x1 +3x2 3x2= 1 5х2 5x2 = 2 + + ·[· (i). calculate -5 3 2 -1 ][ 2 3] 0 21 + 2x2 + 3r3 3x3 = 2r1 +5x2 + 3x3 = 1 21 + 8x3 -2 and -40 16 9 (i). calculate 13 -5-3 5 -2 -1 2 }][ 3 (ii). solve the linear system using the matrix method. 5 12 1 2 3 253 and 108 (ii). solve the linear system using the matrix method. 2 i]. 3 -1 1 2 3 253 1 08 -40 16 9 13 -5 -3 5 -2 -1
8. Express the following linear systems (from) in the form of matrix equations. { (a). (b). 21 2x1 +3x2 3x2= 1 5х2 5x2 = 2 + + ·[· (i). calculate -5 3 2 -1 ][ 2 3] 0 21 + 2x2 + 3r3 3x3 = 2r1 +5x2 + 3x3 = 1 21 + 8x3 -2 and -40 16 9 (i). calculate 13 -5-3 5 -2 -1 2 }][ 3 (ii). solve the linear system using the matrix method. 5 12 1 2 3 253 and 108 (ii). solve the linear system using the matrix method. 2 i]. 3 -1 1 2 3 253 1 08 -40 16 9 13 -5 -3 5 -2 -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show full answers and steps to part a) & b)
![## Problem 8
### Express the following linear systems in the form of matrix equations.
#### (a)
**System of Equations:**
\[
\begin{cases}
x_1 + 3x_2 = 1 \\
2x_1 + 5x_2 = 2
\end{cases}
\]
**Tasks:**
(i) Calculate the matrix product:
\[
\begin{bmatrix}
-5 & 3 \\
2 & -1
\end{bmatrix}
\begin{bmatrix}
1 & 3 \\
2 & 5
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
1 & 3 \\
2 & 5
\end{bmatrix}
\begin{bmatrix}
-5 & 3 \\
2 & -1
\end{bmatrix}
\]
(ii) Solve the linear system using the matrix method.
#### (b)
**System of Equations:**
\[
\begin{cases}
x_1 + 2x_2 + 3x_3 = 0 \\
2x_1 + 5x_2 + 3x_3 = 1 \\
x_1 + 8x_3 = -2
\end{cases}
\]
**Tasks:**
(i) Calculate the matrix product:
\[
\begin{bmatrix}
-40 & 16 & 9 \\
13 & -5 & -3 \\
5 & -2 & -1
\end{bmatrix}
\begin{bmatrix}
1 & 2 & 3 \\
2 & 5 & 3 \\
1 & 0 & 8
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
1 & 2 & 3 \\
2 & 5 & 3 \\
1 & 0 & 8
\end{bmatrix}
\begin{bmatrix}
-40 & 16 & 9 \\
13 & -5 & -3 \\
5 & -2 & -1
\end{bmatrix}
\]
(ii) Solve the linear system using the matrix method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2F74e7b18a-d5b9-470d-8a82-334cd1110d43%2F13wx8i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem 8
### Express the following linear systems in the form of matrix equations.
#### (a)
**System of Equations:**
\[
\begin{cases}
x_1 + 3x_2 = 1 \\
2x_1 + 5x_2 = 2
\end{cases}
\]
**Tasks:**
(i) Calculate the matrix product:
\[
\begin{bmatrix}
-5 & 3 \\
2 & -1
\end{bmatrix}
\begin{bmatrix}
1 & 3 \\
2 & 5
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
1 & 3 \\
2 & 5
\end{bmatrix}
\begin{bmatrix}
-5 & 3 \\
2 & -1
\end{bmatrix}
\]
(ii) Solve the linear system using the matrix method.
#### (b)
**System of Equations:**
\[
\begin{cases}
x_1 + 2x_2 + 3x_3 = 0 \\
2x_1 + 5x_2 + 3x_3 = 1 \\
x_1 + 8x_3 = -2
\end{cases}
\]
**Tasks:**
(i) Calculate the matrix product:
\[
\begin{bmatrix}
-40 & 16 & 9 \\
13 & -5 & -3 \\
5 & -2 & -1
\end{bmatrix}
\begin{bmatrix}
1 & 2 & 3 \\
2 & 5 & 3 \\
1 & 0 & 8
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
1 & 2 & 3 \\
2 & 5 & 3 \\
1 & 0 & 8
\end{bmatrix}
\begin{bmatrix}
-40 & 16 & 9 \\
13 & -5 & -3 \\
5 & -2 & -1
\end{bmatrix}
\]
(ii) Solve the linear system using the matrix method.
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