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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=

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=

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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Advanced Math - Inverse of a Matrix

Solve the given equation, an example is shown in 2nd 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
4. Write the system in the form AX = B. Use the X-A-¹B to solve for each matrix B. 7x1-2x2 = b1 3x1-2x2 = b₁ (5) B=
Transcribed Image Text:4. Write the system in the form AX = B. Use the X-A-¹B to solve for each matrix B. 7x1-2x2 = b1 3x1-2x2 = b₁ (5) B=
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