144 Use the fact that the matrices 1 5 4 145 to solve the following system of linear equations. x + 4y + 4z = - 37 x+ 5y + 4z = -40 x + 4y + 5z = - 45 and 9 - 1 -1 -4 -4 1 0 0 are inverses of each other 1
144 Use the fact that the matrices 1 5 4 145 to solve the following system of linear equations. x + 4y + 4z = - 37 x+ 5y + 4z = -40 x + 4y + 5z = - 45 and 9 - 1 -1 -4 -4 1 0 0 are inverses of each other 1
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
![Use the fact that the matrices
\[
\begin{bmatrix}
1 & 4 & 4 \\
1 & 5 & 4 \\
1 & 4 & 5
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
9 & -4 & -4 \\
-1 & 1 & 0 \\
-1 & 0 & 1
\end{bmatrix}
\]
are inverses of each other to solve the following system of linear equations.
\[
\begin{cases}
x + 4y + 4z = -37 \\
x + 5y + 4z = -40 \\
x + 4y + 5z = -45
\end{cases}
\]
The solution is \( x = \boxed{\phantom{0}}, \, y = \boxed{\phantom{0}}, \, \text{and} \, z = \boxed{\phantom{0}} \).
(Type integers or simplified fractions.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4726056b-a0d8-4167-a534-8f03670a441a%2F1e8639e0-a3a5-4bc2-aa05-155fd076e4d7%2Faiioycc_processed.png&w=3840&q=75)
Transcribed Image Text:Use the fact that the matrices
\[
\begin{bmatrix}
1 & 4 & 4 \\
1 & 5 & 4 \\
1 & 4 & 5
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
9 & -4 & -4 \\
-1 & 1 & 0 \\
-1 & 0 & 1
\end{bmatrix}
\]
are inverses of each other to solve the following system of linear equations.
\[
\begin{cases}
x + 4y + 4z = -37 \\
x + 5y + 4z = -40 \\
x + 4y + 5z = -45
\end{cases}
\]
The solution is \( x = \boxed{\phantom{0}}, \, y = \boxed{\phantom{0}}, \, \text{and} \, z = \boxed{\phantom{0}} \).
(Type integers or simplified fractions.)
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