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(f) X- x2+23 = 4 X2+2x3 =4 %3D 2x1 + 3x2- X3 = 1 7x + 3x2 +4x3 =7

(f) X- x2+23 = 4 X2+2x3 =4 %3D 2x1 + 3x2- X3 = 1 7x + 3x2 +4x3 =7

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Question (f)
0 1 3 4] 5-2 0. 0. (k) (e) 0. 0. 0. 0. 01 0. 01 01 0 • 0 0 1 -1 (1) 0 00 4. For each of the systems in Exercise 3, make a list of the lead variables and a second list of the free variables. 5. For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is consistent. If the system is consistent and involves no free variables, use back substitution to find the unique solution. If the system is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. 6. Use C follow (a) (b) 2 3. (b) 2-3x2 = 5 -4x +6x2 8 (a) X 2x2 3 2r - 2 =9 (c) X1 (c) (d) 3x+2x2- X3= 4 2r + 3x2 0 X1- 2r2+2r3= 1 1 1x+ 2x2+ x3= 14 3x-2r2 0 (d) x 2r (e) 2r +3x2+ X3 = 1 X1 3x +4x2 + 2r3 = 4 7. Give a eous line three un (f) X- x2+2z = 4 2x1 +3x2- X3 = 1 7x) + 3x2 + 4x3 = 7 tions. W of a nonh geometric
Transcribed Image Text:0 1 3 4] 5-2 0. 0. (k) (e) 0. 0. 0. 0. 01 0. 01 01 0 • 0 0 1 -1 (1) 0 00 4. For each of the systems in Exercise 3, make a list of the lead variables and a second list of the free variables. 5. For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is consistent. If the system is consistent and involves no free variables, use back substitution to find the unique solution. If the system is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. 6. Use C follow (a) (b) 2 3. (b) 2-3x2 = 5 -4x +6x2 8 (a) X 2x2 3 2r - 2 =9 (c) X1 (c) (d) 3x+2x2- X3= 4 2r + 3x2 0 X1- 2r2+2r3= 1 1 1x+ 2x2+ x3= 14 3x-2r2 0 (d) x 2r (e) 2r +3x2+ X3 = 1 X1 3x +4x2 + 2r3 = 4 7. Give a eous line three un (f) X- x2+2z = 4 2x1 +3x2- X3 = 1 7x) + 3x2 + 4x3 = 7 tions. W of a nonh geometric
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