To determine To calculate: The solution of the system of equations, x + y + z = 2 , − 2 x − y + z = 1 and x − 2 y − z = 1 by addition method. Explanation Given Information: The system of equations, x + y + z = 2 , − 2 x − y + z = 1 and x − 2 y − z = 1 . Formula used: Addition method to solve a linear system of equations: Step1. Write the equations in the form of a x + b y + c z = d . Step2. Eliminate the one variable by using the any two equations by multiplying one or both equations by a constant, so that after adding the equations, there will be equation of two variables. Step3: Repeat the step2 with one different equation for eliminating the same variable. Step4. Write the both new equations in the form of a x + b y = c . Step5. Multiply one or both equations by a constant, so that after adding the equations, there will be only one variable. Step6. Add both the equations which will result in equation of one variable. Step7. Compute the equation obtained in step6 and find the value of one variable. Step8. Substitute the value obtained in step7 of one variable in any of the new equation of two variables to obtain other one. Step9. Substitute the value obtained in the step7 and step8 in any of the original equation to obtain the third one. Step10. Write the value of variables in correct order. Step11. Check the solution by putting the calculated value in all equations in the system. Calculation: Consider the system of equations: x + y + z = 2 …… ( 1 ) − 2 x − y + z = 1 …… ( 2 ) x − 2 y − z = 1 …… ( 3 ) Use equation ( 1 ) and equation ( 2 ) to eliminate x : Multiply equation ( 1 ) by 2 and add with equation ( 2 ) as; 2 x + 2 y + 2 z = 4 − 2 x − y + z = 1 _ y + 3 z = 5 Therefore, the new equation will be, y + 3 z = 5 …… ( 4 ) Use equation ( 2 ) and equation ( 3 ) to eliminate x : Multiply equation ( 3 ) by 2 and add with equation ( 1 ) as; − 2 x − y + z = 1 2 x − 4 y − 2 z = 2 _ − 5 y − z = 3 Therefore, the new equation will be, − 5 y − z = 3 …… ( 5 ) Use equation ( 4 ) and equation ( 5 ) to eliminate y and solve for z : Multiply equation ( 4 ) by 5 and add with equation ( 5 ) as; 5y + 15 z = 25 − 5 y − z = 3 _ 14 z = 28 z = 2 Thus, the value of z is 2

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4, Problem 12PT

To determine

To calculate: The solution of the system of equations, x+y+z=2, −2x−y+z=1 and x−2y−z=1 by addition method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 11PT

Chapter 4, Problem 13PT

Students have asked these similar questions

You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods

Plane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)

show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45

Chapter 4 Solutions

Intermediate Algebra For College Students (10th Edition)

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.