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Exercise 1 Which of the following equations are linear in the variables x,y,z 1 - 2x + 3y – 22 = 2, 2 - 3/2x + Ty – z = -1, 4 - x - y + e = 0, 3 - (r – 1)2 + (y + 1)² – a² – y² = z.

Exercise 1 Which of the following equations are linear in the variables x,y,z 1 - 2x + 3y – 22 = 2, 2 - 3/2x + Ty – z = -1, 4 - x - y + e = 0, 3 - (r – 1)2 + (y + 1)² – a² – y² = z.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 1CE
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Exercise 1 Which of the following equations are linear in the variables x,y,z 1 - 2.x + 3y- z? = 2, 2 - 3/2.x + Ty – z = -1, 4 - x - y+e = 0, 3 - (r – 1)? + (y + 1)? – 2? – y? = z. Exercise 2 Give the solution set of the following linear equations of unknowns x, y, z. 1 - x + y – z = 1 2 - 2л - Зу %3 5. Exercise 3 To solve a system of linear equations, recall the steps operators applying on equa- tions and on the rows of the corresponding matrix. Using these operations to solve the following system x1 + x2 - 2x3 = 1, X1 + x2 + x3 = 0, 4.x1 – x3 = 4, Exercise 4 Find the augmented matrices of the following linear systems 3.x1 + x2 – x3 = 2, T1 - x2 +x3= 5, 4.x2 + x3 = 0, T1 - x2 + 2.x3 +x3 = 1, x2 - x4 = -1, Exercise 5 Characterise the row echelon form matrices and reduced row echelon form matrices. Put the following matrices in reduced row echelon forms using Gauss-Jordan elimi- nation 0 2 3 -3 0 1 A = 35 6 В — -1 5 89, 6. 2 7
Transcribed Image Text:Exercise 1 Which of the following equations are linear in the variables x,y,z 1 - 2.x + 3y- z? = 2, 2 - 3/2.x + Ty – z = -1, 4 - x - y+e = 0, 3 - (r – 1)? + (y + 1)? – 2? – y? = z. Exercise 2 Give the solution set of the following linear equations of unknowns x, y, z. 1 - x + y – z = 1 2 - 2л - Зу %3 5. Exercise 3 To solve a system of linear equations, recall the steps operators applying on equa- tions and on the rows of the corresponding matrix. Using these operations to solve the following system x1 + x2 - 2x3 = 1, X1 + x2 + x3 = 0, 4.x1 – x3 = 4, Exercise 4 Find the augmented matrices of the following linear systems 3.x1 + x2 – x3 = 2, T1 - x2 +x3= 5, 4.x2 + x3 = 0, T1 - x2 + 2.x3 +x3 = 1, x2 - x4 = -1, Exercise 5 Characterise the row echelon form matrices and reduced row echelon form matrices. Put the following matrices in reduced row echelon forms using Gauss-Jordan elimi- nation 0 2 3 -3 0 1 A = 35 6 В — -1 5 89, 6. 2 7
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