10. a b C d a + 3b = c b+c+a=d

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary
### Problem 10

Given the vector:

\[
\begin{bmatrix}
a \\
b \\
c \\
d
\end{bmatrix}
\]

The following system of equations needs to be satisfied:

1. \( a + 3b = c \)
2. \( b + c + a = d \)

These equations represent a set of simultaneous linear equations that describe the relationships between the variables \(a\), \(b\), \(c\), and \(d\). To find the values of these variables, substitution or matrix methods can be used. This system can help in understanding how to manipulate and solve linear equations in vector form.
Transcribed Image Text:### Problem 10 Given the vector: \[ \begin{bmatrix} a \\ b \\ c \\ d \end{bmatrix} \] The following system of equations needs to be satisfied: 1. \( a + 3b = c \) 2. \( b + c + a = d \) These equations represent a set of simultaneous linear equations that describe the relationships between the variables \(a\), \(b\), \(c\), and \(d\). To find the values of these variables, substitution or matrix methods can be used. This system can help in understanding how to manipulate and solve linear equations in vector form.
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