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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
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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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.)
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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