Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. Use an inverse matrix to solve the given system of equations X1 + x₂ =4 2x1-x2 = 14

3. Use an inverse matrix to solve the given system of equations X1 + x₂ =4 2x1-x2 = 14

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
See similar textbooks
icon
Related questions
Question

Advanced Math - Inverse of a Matrix

Solve the given equations. Example is in the second pic. 

The inverse of a matrix can be used to solve a system of linear equations. Suppose we have a system of m linear equations in n variables, X1, X2,...,Xn a11x1 + a12X2 + ... + a1nxn = b₁ a21x1 + a22x2 + + a2nxn = b₂ a31x1 + a32x2+...+ a3nxn = b3 which can be written as a matrix equation AX = B where A = a11 a 12 a21 a22 : ... ain a2n : X = 6 9 (²-3) - (²32) 36 39 21 X2 am1 am2 ... amn Since A ¹A = I and IX = X, we have X = A¹¹B. Example Use the inverse of the coefficient matrix to solve the system. 2x - 9y = 15 3x + 6y = 16 Solution 2 9 15 (3-3) ()-(5) = 6 16 First we obtain the inverse of A-¹ B In 6 9 15 (:) - * (32) (5) - +(²4) - (9) (233) = = 16 39 Thus obtaining the value of x = 6 and y = -1/3 b1 b2 : bm
Transcribed Image Text:The inverse of a matrix can be used to solve a system of linear equations. Suppose we have a system of m linear equations in n variables, X1, X2,...,Xn a11x1 + a12X2 + ... + a1nxn = b₁ a21x1 + a22x2 + + a2nxn = b₂ a31x1 + a32x2+...+ a3nxn = b3 which can be written as a matrix equation AX = B where A = a11 a 12 a21 a22 : ... ain a2n : X = 6 9 (²-3) - (²32) 36 39 21 X2 am1 am2 ... amn Since A ¹A = I and IX = X, we have X = A¹¹B. Example Use the inverse of the coefficient matrix to solve the system. 2x - 9y = 15 3x + 6y = 16 Solution 2 9 15 (3-3) ()-(5) = 6 16 First we obtain the inverse of A-¹ B In 6 9 15 (:) - * (32) (5) - +(²4) - (9) (233) = = 16 39 Thus obtaining the value of x = 6 and y = -1/3 b1 b2 : bm
3. Use an inverse matrix to solve the given system of equations X1 + x₂ =4 2x1-x2 = 14 4. Write the system in the form AX = B. Use the X-A¹B to solve for each matrix B. 7x1-2x2 = b₁ 3x1-2x2 = b₁ 5 B-(1)
Transcribed Image Text:3. Use an inverse matrix to solve the given system of equations X1 + x₂ =4 2x1-x2 = 14 4. Write the system in the form AX = B. Use the X-A¹B to solve for each matrix B. 7x1-2x2 = b₁ 3x1-2x2 = b₁ 5 B-(1)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS