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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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Calculate :
a) Using Matrix E , is (X1 + X2 , X3) independent (show work)
b) Using Matrix E , is (⅓ X1 + X2 + ⅓ X3, X1) independent (show work)
![### Matrices Overview
#### Matrix A
Matrix \( A \) is a \( 2 \times 2 \) matrix:
\[
A = \begin{bmatrix}
7 & 3 \\
1 & 2
\end{bmatrix}
\]
#### Matrix B
Matrix \( B \) is a \( 3 \times 2 \) matrix:
\[
B = \begin{bmatrix}
1 & -1 \\
2 & 3 \\
1 & 3
\end{bmatrix}
\]
#### Matrix C
Matrix \( C \) is a \( 3 \times 1 \) column matrix:
\[
C = \begin{bmatrix}
2 \\
1 \\
4
\end{bmatrix}
\]
#### Matrix D
Matrix \( D \) is a \( 2 \times 2 \) matrix with fractional elements:
\[
D = \begin{bmatrix}
\frac{1}{2} & \frac{3}{2} \\
\frac{5}{6} & \frac{1}{3}
\end{bmatrix}
\]
#### Matrix E
Matrix \( E \) is a \( 3 \times 3 \) matrix:
\[
E = \begin{bmatrix}
4 & 1 & 1 \\
4 & 9 & 3 \\
8 & 6 & 4
\end{bmatrix}
\]
#### Matrix Σ
Matrix \( \Sigma \) is a \( 3 \times 3 \) matrix:
\[
\Sigma = \begin{bmatrix}
3 & 1 & 0 \\
1 & 2 & 4 \\
0 & 4 & 2
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee7f2922-58de-4beb-945a-187f9fc8c1de%2Fd6de594d-f035-40a4-a81b-9cf7c770d268%2Fqukrc3b_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrices Overview
#### Matrix A
Matrix \( A \) is a \( 2 \times 2 \) matrix:
\[
A = \begin{bmatrix}
7 & 3 \\
1 & 2
\end{bmatrix}
\]
#### Matrix B
Matrix \( B \) is a \( 3 \times 2 \) matrix:
\[
B = \begin{bmatrix}
1 & -1 \\
2 & 3 \\
1 & 3
\end{bmatrix}
\]
#### Matrix C
Matrix \( C \) is a \( 3 \times 1 \) column matrix:
\[
C = \begin{bmatrix}
2 \\
1 \\
4
\end{bmatrix}
\]
#### Matrix D
Matrix \( D \) is a \( 2 \times 2 \) matrix with fractional elements:
\[
D = \begin{bmatrix}
\frac{1}{2} & \frac{3}{2} \\
\frac{5}{6} & \frac{1}{3}
\end{bmatrix}
\]
#### Matrix E
Matrix \( E \) is a \( 3 \times 3 \) matrix:
\[
E = \begin{bmatrix}
4 & 1 & 1 \\
4 & 9 & 3 \\
8 & 6 & 4
\end{bmatrix}
\]
#### Matrix Σ
Matrix \( \Sigma \) is a \( 3 \times 3 \) matrix:
\[
\Sigma = \begin{bmatrix}
3 & 1 & 0 \\
1 & 2 & 4 \\
0 & 4 & 2
\end{bmatrix}
\]
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