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solve each set of equations by the method of finding the inverse of the coefficient matrix. Hint: See Example 3. y + z = 4 2x + y - z = -1 3x + 2y + 2z

solve each set of equations by the method of finding the inverse of the coefficient matrix. Hint: See Example 3. y + z = 4 2x + y - z = -1 3x + 2y + 2z

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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solve each set of equations by the method of finding the inverse of the coefficient matrix. Hint: See Example 3. y + z = 4 2x + y z = -1 3x + 2y + 2z =
Transcribed Image Text:solve each set of equations by the method of finding the inverse of the coefficient matrix. Hint: See Example 3. y + z = 4 2x + y z = -1 3x + 2y + 2z =
• Example 3. For the matrix M of the coefficients in equations (6.7) or (6.9), find M-1. 1 0 -1 M = -2 3 1 -3 2 We find det M = 3. The cofactors of the elements are: 3 0 = 6, -3 2 -2 0 = 4, -2 1st row : 3 = 3. 1 2 1 -3 1 1 1 2nd = 3, = 3, = 3. -3 row : -3 2 2 |0 1 0 = 3. -2 3 -1 1 - 3rd row : - 3, 2, -2 Then 6 4 3 C = 1 CT det M 6 3 3 1 4 3 2 3 3 3 3 3 3 3 so M-1 - = - 3 2 3 Now we can use M-1 to solve equations (6.9). By (6.12), the solution is given by the column matrix r = M-'k, so we have 6 3 3 1 4 3 2 3 3 3 3, -10 or x = 1, y = 1, z = -4. (See Problem 12.)
Transcribed Image Text:• Example 3. For the matrix M of the coefficients in equations (6.7) or (6.9), find M-1. 1 0 -1 M = -2 3 1 -3 2 We find det M = 3. The cofactors of the elements are: 3 0 = 6, -3 2 -2 0 = 4, -2 1st row : 3 = 3. 1 2 1 -3 1 1 1 2nd = 3, = 3, = 3. -3 row : -3 2 2 |0 1 0 = 3. -2 3 -1 1 - 3rd row : - 3, 2, -2 Then 6 4 3 C = 1 CT det M 6 3 3 1 4 3 2 3 3 3 3 3 3 3 so M-1 - = - 3 2 3 Now we can use M-1 to solve equations (6.9). By (6.12), the solution is given by the column matrix r = M-'k, so we have 6 3 3 1 4 3 2 3 3 3 3, -10 or x = 1, y = 1, z = -4. (See Problem 12.)
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