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19. 2x + 2y + 4z = 0 w - y - 3z = 0 2w + 3x + y + z = 0 -2w + x + 3y - 2z = 0

19. 2x + 2y + 4z = 0 w - y - 3z = 0 2w + 3x + y + z = 0 -2w + x + 3y - 2z = 0

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter9: Solving Quadratic Functions
Section9.6: Solving Nonlinear Systems Of Equations
Problem 33E
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Only Question 19 and 40 please on paper. Thanks a lot.
2. 4x3 = 0 In Exercises 15-22, solve the given linear system by any method. 16. 2x - y - 3z = 0 15. 2x₁ + x₂ + 3x3 = 0 X₁ + 2x₂ = 0 -x + 2y3z = 0 X₂ + x3 = 0 x + y + 4z = 0 v + 3w - 2x = 0 17. 3x₁ + x₂ + x3 + x4 = 0 5x₁x₂ + x3 - X4 = 0 2u+v4w + 3x = 0 2u+30+2w - x = 0 -4u- 30 + 5w - 4x = 0 19. 2x + 2y + 4z = 0 W - y 3z = 0 2w + 3x + y + z = 0 -2w + x + 3y - 2z = 0 + x₁ = 0 x₁ + 4x₂ + 2x3 = 0 - 2x₂ - 2x3 - X4 = 0 2x₁4x₂ + x3 + x₁ = 0 x₁2x₂x3 + x4 = 0 = 9 - 213 + 714 = 11 31₁ 31₂ +13 + 514 = 8 21₁ + 1₂ +413 + 414 = 10 Z3+ Z₁ + Z5 = 0 -Z₁ - Z₂ +2Z3 - 3Z4 + Z5 = 0 Z₁ + Z₂-2Z3 -Z₁ = 0 2Z₁ + 2Z₂ - Z3 + Z₁ = 0 In each part of Exercises 23-24, the augmented matrix for a lin- ear system is given in which the asterisk represents an unspecified ing whather the system is consistent, and if so is not 20. x₁ + 3x₂ 21. 21₁-1₂ + 313 + 414 I₁ 18. 22.
Transcribed Image Text:2. 4x3 = 0 In Exercises 15-22, solve the given linear system by any method. 16. 2x - y - 3z = 0 15. 2x₁ + x₂ + 3x3 = 0 X₁ + 2x₂ = 0 -x + 2y3z = 0 X₂ + x3 = 0 x + y + 4z = 0 v + 3w - 2x = 0 17. 3x₁ + x₂ + x3 + x4 = 0 5x₁x₂ + x3 - X4 = 0 2u+v4w + 3x = 0 2u+30+2w - x = 0 -4u- 30 + 5w - 4x = 0 19. 2x + 2y + 4z = 0 W - y 3z = 0 2w + 3x + y + z = 0 -2w + x + 3y - 2z = 0 + x₁ = 0 x₁ + 4x₂ + 2x3 = 0 - 2x₂ - 2x3 - X4 = 0 2x₁4x₂ + x3 + x₁ = 0 x₁2x₂x3 + x4 = 0 = 9 - 213 + 714 = 11 31₁ 31₂ +13 + 514 = 8 21₁ + 1₂ +413 + 414 = 10 Z3+ Z₁ + Z5 = 0 -Z₁ - Z₂ +2Z3 - 3Z4 + Z5 = 0 Z₁ + Z₂-2Z3 -Z₁ = 0 2Z₁ + 2Z₂ - Z3 + Z₁ = 0 In each part of Exercises 23-24, the augmented matrix for a lin- ear system is given in which the asterisk represents an unspecified ing whather the system is consistent, and if so is not 20. x₁ + 3x₂ 21. 21₁-1₂ + 313 + 414 I₁ 18. 22.
the 27, X, Y, = y², U has only the trivial solution, what can be said about the solu- tions of the following system? a₁x + b₁y+c₁z = 3 a₂x-b₂y + c₂z = 7 a3x + b3y - c₂z = 11 40. a. If A is a matrix with three rows and five columns, then what is the maximum possible number of leading 1's in its reduced row echelon form? b. If B is a matrix with three rows and six columns, then what is the maximum possible number of parameters in the general solution of the linear system with augmented matrix B? c. If C is a matrix with five rows and three columns, then what is the minimum possible number of rows of zeros in any row echelon form of C? 41. Describe all possible reduced row echelon forms of a b С d a b с e f g h d f a. e b.
Transcribed Image Text:the 27, X, Y, = y², U has only the trivial solution, what can be said about the solu- tions of the following system? a₁x + b₁y+c₁z = 3 a₂x-b₂y + c₂z = 7 a3x + b3y - c₂z = 11 40. a. If A is a matrix with three rows and five columns, then what is the maximum possible number of leading 1's in its reduced row echelon form? b. If B is a matrix with three rows and six columns, then what is the maximum possible number of parameters in the general solution of the linear system with augmented matrix B? c. If C is a matrix with five rows and three columns, then what is the minimum possible number of rows of zeros in any row echelon form of C? 41. Describe all possible reduced row echelon forms of a b С d a b с e f g h d f a. e b.
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