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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

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 32E
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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)
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