write 4 Given that = 3 -5 4 2 3 4 as a linear combination of the vectors -5 4 -5+ -5 3 3 -2 5 -4 -3 -5 5 2 3 + 3 -2 -4 0 1 0 0 1 - - 27 23 125 23 166 23 [3]
write 4 Given that = 3 -5 4 2 3 4 as a linear combination of the vectors -5 4 -5+ -5 3 3 -2 5 -4 -3 -5 5 2 3 + 3 -2 -4 0 1 0 0 1 - - 27 23 125 23 166 23 [3]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Given that
\[
\begin{bmatrix}
3 & -5 & 3 & 2 \\
-5 & 3 & -2 & 4 \\
4 & 5 & -4 & -3
\end{bmatrix}
\sim
\begin{bmatrix}
1 & 0 & 0 & -\frac{27}{23} \\
0 & 1 & 0 & -\frac{125}{23} \\
0 & 0 & 1 & -\frac{166}{23}
\end{bmatrix},
\]
write
\[
\begin{bmatrix}
2 \\
4 \\
-3
\end{bmatrix}
\]
as a linear combination of the vectors
\[
\begin{bmatrix}
3 \\
-5 \\
4
\end{bmatrix},
\begin{bmatrix}
-5 \\
3 \\
5
\end{bmatrix},
\begin{bmatrix}
3 \\
-2 \\
-4
\end{bmatrix}.
\]
\[
\begin{bmatrix}
2 \\
4 \\
-3
\end{bmatrix}
=
\boxed{}
\begin{bmatrix}
3 \\
-5 \\
4
\end{bmatrix}
+
\boxed{}
\begin{bmatrix}
-5 \\
3 \\
5
\end{bmatrix}
+
\boxed{}
\begin{bmatrix}
3 \\
-2 \\
-4
\end{bmatrix}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F329038e6-522f-4245-8c94-7b937a205b4b%2Fb58b883d-f7fa-46d3-bd54-940049acffa1%2Fbr8wdnc_processed.png&w=3840&q=75)
Transcribed Image Text:Given that
\[
\begin{bmatrix}
3 & -5 & 3 & 2 \\
-5 & 3 & -2 & 4 \\
4 & 5 & -4 & -3
\end{bmatrix}
\sim
\begin{bmatrix}
1 & 0 & 0 & -\frac{27}{23} \\
0 & 1 & 0 & -\frac{125}{23} \\
0 & 0 & 1 & -\frac{166}{23}
\end{bmatrix},
\]
write
\[
\begin{bmatrix}
2 \\
4 \\
-3
\end{bmatrix}
\]
as a linear combination of the vectors
\[
\begin{bmatrix}
3 \\
-5 \\
4
\end{bmatrix},
\begin{bmatrix}
-5 \\
3 \\
5
\end{bmatrix},
\begin{bmatrix}
3 \\
-2 \\
-4
\end{bmatrix}.
\]
\[
\begin{bmatrix}
2 \\
4 \\
-3
\end{bmatrix}
=
\boxed{}
\begin{bmatrix}
3 \\
-5 \\
4
\end{bmatrix}
+
\boxed{}
\begin{bmatrix}
-5 \\
3 \\
5
\end{bmatrix}
+
\boxed{}
\begin{bmatrix}
3 \\
-2 \\
-4
\end{bmatrix}.
\]
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