Solve the following system of equations by using the inverse of the coefficient matrix. The inverse of the coefficient matrix is shown. x - 2y + 3z 0 y- z+ W = -8 - 2x + 2y - 2z+ 4w = 10 2y3z + W = -1 Using the variables and values in the system of equations, what is the matrix equation solved for the matrix of the variables? O A. O B. U -|N -IN NI → N|→ -1 4 1 1 1 2 NIG 5 دام 2 2 دان 1 1 4 2 - IN 2 -2 NI N/W C Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The solution of the system is (...). (Simplify your answers.) OB. There are infinitely many solutions. The solutions are x = (Use integers or fractions for any numbers in the expression.) y= U and z= where w is any real number. 1 1 1 2 4 -|2 -1 4 - IN 5|2 -N -IN داد -14 ヤーレ N|→ N 1 1 1 N/W NI→ f NI→ -1 4 1 NÍ → 2 1 FIN -14 -|N -IN 2 - 10 12 IN -14 1 ➤|→ N NIW BIN -IN 1
Solve the following system of equations by using the inverse of the coefficient matrix. The inverse of the coefficient matrix is shown. x - 2y + 3z 0 y- z+ W = -8 - 2x + 2y - 2z+ 4w = 10 2y3z + W = -1 Using the variables and values in the system of equations, what is the matrix equation solved for the matrix of the variables? O A. O B. U -|N -IN NI → N|→ -1 4 1 1 1 2 NIG 5 دام 2 2 دان 1 1 4 2 - IN 2 -2 NI N/W C Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The solution of the system is (...). (Simplify your answers.) OB. There are infinitely many solutions. The solutions are x = (Use integers or fractions for any numbers in the expression.) y= U and z= where w is any real number. 1 1 1 2 4 -|2 -1 4 - IN 5|2 -N -IN داد -14 ヤーレ N|→ N 1 1 1 N/W NI→ f NI→ -1 4 1 NÍ → 2 1 FIN -14 -|N -IN 2 - 10 12 IN -14 1 ➤|→ N NIW BIN -IN 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
![**Solving a System of Equations Using the Inverse of a Coefficient Matrix**
To solve the following system of equations using the inverse of the coefficient matrix, we have the inverse of the coefficient matrix provided:
\[
x - 2y + 3z = 0
\]
\[
y - z + w = -8
\]
\[
-2x + 2y - 2z + 4w = 10
\]
\[
2y - 3z + w = -1
\]
The inverse of the coefficient matrix \(A^{-1}\) is given as:
\[
A^{-1} =
\begin{bmatrix}
\frac{1}{2} & 1 & \frac{1}{2} & 1 \\
\frac{1}{2} & 4 & -\frac{1}{2} & -2 \\
-\frac{1}{2} & 5 & \frac{1}{4} & -\frac{3}{2} \\
\frac{1}{2} & -\frac{1}{2} & \frac{1}{4} & \frac{1}{2}
\end{bmatrix}
\]
**Matrix Equation for the System of Equations**
Using the variables and values in the system of equations, identify the matrix equation for the variables. The task is to select the correct representation of the system:
- Option A:
\[
\begin{bmatrix}
\frac{1}{2} & 1 & \frac{1}{2} & 1 \\
\frac{1}{2} & 4 & -\frac{1}{2} & -2 \\
-\frac{1}{2} & 5 & \frac{1}{4} & -\frac{3}{2} \\
\frac{1}{2} & -\frac{1}{2} & \frac{1}{4} & \frac{1}{2}
\end{bmatrix}
\begin{bmatrix}
x \\
y \\
z \\
w
\end{bmatrix}
=
\begin{bmatrix}
0 \\
-8 \\
10 \\
-1
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc62debf9-2696-4946-934a-f308bf93cf3b%2F7e64c4f6-c3ef-49cb-b194-6bf2c2b3b02f%2Fas33aj_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving a System of Equations Using the Inverse of a Coefficient Matrix**
To solve the following system of equations using the inverse of the coefficient matrix, we have the inverse of the coefficient matrix provided:
\[
x - 2y + 3z = 0
\]
\[
y - z + w = -8
\]
\[
-2x + 2y - 2z + 4w = 10
\]
\[
2y - 3z + w = -1
\]
The inverse of the coefficient matrix \(A^{-1}\) is given as:
\[
A^{-1} =
\begin{bmatrix}
\frac{1}{2} & 1 & \frac{1}{2} & 1 \\
\frac{1}{2} & 4 & -\frac{1}{2} & -2 \\
-\frac{1}{2} & 5 & \frac{1}{4} & -\frac{3}{2} \\
\frac{1}{2} & -\frac{1}{2} & \frac{1}{4} & \frac{1}{2}
\end{bmatrix}
\]
**Matrix Equation for the System of Equations**
Using the variables and values in the system of equations, identify the matrix equation for the variables. The task is to select the correct representation of the system:
- Option A:
\[
\begin{bmatrix}
\frac{1}{2} & 1 & \frac{1}{2} & 1 \\
\frac{1}{2} & 4 & -\frac{1}{2} & -2 \\
-\frac{1}{2} & 5 & \frac{1}{4} & -\frac{3}{2} \\
\frac{1}{2} & -\frac{1}{2} & \frac{1}{4} & \frac{1}{2}
\end{bmatrix}
\begin{bmatrix}
x \\
y \\
z \\
w
\end{bmatrix}
=
\begin{bmatrix}
0 \\
-8 \\
10 \\
-1
\end{bmatrix}
\]
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
