= Solve the matrix equation AX = B for X. 14 -4 B= A=[-33] ³- (-22) -8 X=
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
![**Title: Solving Matrix Equation AX = B**
**Objective:** Solve the matrix equation \( AX = B \) for \( X \).
**Given:**
\[ A = \begin{bmatrix} 1 & 4 \\ -3 & 5 \end{bmatrix} \]
\[ B = \begin{bmatrix} -4 \\ -22 \end{bmatrix} \]
**Solution:**
To find \( X \), we need to compute the inverse of matrix \( A \) (denoted as \( A^{-1} \)) and then multiply it by \( B \). The formula used is:
\[ X = A^{-1}B \]
**X =**
\[ \begin{bmatrix} \text{[ ]} \\ \text{[ ]} \end{bmatrix} \]
**Instructions:**
1. Calculate the determinant of \( A \).
2. Find the inverse of \( A \) if the determinant is non-zero.
3. Multiply \( A^{-1} \) by \( B \) to get \( X \).
**Conclusion:**
This process will yield the solution \( X \) in matrix form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c391909-e4e2-4c58-85bb-5bea7cb900f2%2Ffa223fad-5621-49d1-937d-968e4d230df5%2Fay6n3e6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving Matrix Equation AX = B**
**Objective:** Solve the matrix equation \( AX = B \) for \( X \).
**Given:**
\[ A = \begin{bmatrix} 1 & 4 \\ -3 & 5 \end{bmatrix} \]
\[ B = \begin{bmatrix} -4 \\ -22 \end{bmatrix} \]
**Solution:**
To find \( X \), we need to compute the inverse of matrix \( A \) (denoted as \( A^{-1} \)) and then multiply it by \( B \). The formula used is:
\[ X = A^{-1}B \]
**X =**
\[ \begin{bmatrix} \text{[ ]} \\ \text{[ ]} \end{bmatrix} \]
**Instructions:**
1. Calculate the determinant of \( A \).
2. Find the inverse of \( A \) if the determinant is non-zero.
3. Multiply \( A^{-1} \) by \( B \) to get \( X \).
**Conclusion:**
This process will yield the solution \( X \) in matrix form.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
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,
