Describe the solutions of the given system into parametric vector form. x1+x2+ 2x3= 9 2x1+ 4x2−3x3= 1 3x1+ 3x2+ 6x3= 27 Also compare this solution, geometrically, with the solution set of the following homogeneous system. x1+x2+ 2x3= 0 2x1+ 4x2−3x3= 0 3x1+ 3x2+ 6x3= 0

Describe the solutions of the given system into parametric vector form. x1+x2+ 2x3= 9 2x1+ 4x2−3x3= 1 3x1+ 3x2+ 6x3= 27 Also compare this solution, geometrically, with the solution set of the following homogeneous system. x1+x2+ 2x3= 0 2x1+ 4x2−3x3= 0 3x1+ 3x2+ 6x3= 0

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.2: Guassian Elimination And Matrix Methods

Problem 86E

See similar textbooks

Related questions

Q: Find all solutions, if any, to the given system of equations. Express your answer in vector form. +…

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

Q: Describe all solutions of Ax 0 in parametric vector form, where A is row equivalent to the given…

Q: In Exercises 5 and 6, write a system of equations that is equivalent to the given vector equation.

A: First we simplify the left side using the properties of matrix.

Q: Give the parametric vector form of the general solution of the following system of linear equations:…

Q: Consider the following nonhomogeneous linear system: xi = 2x1 – x2 + t? - x2 = 3x1 – 2x2 + t | 2.…

Q: 1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k…

A: Here the given matrices are A=abcd and B=dcba We have to show…

Q: Consider the system of equations below = 0 X1 – 2x1 – x3 + 3x4 -2x1 + 4x2 + 5x3 - 5x4 3x1 – 6x2 –…

A: Topic : Linear algebra As per our guidelines, At a time only one question will be answered.

Q: Give the parametric vector form of the general solution of the following system of equations: -4…

A: The solution is given as

Q: Find a basis for the solution set to the following homogeneous linear system: + 2x2 + 5x2 + 7r2 2x3…

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

Q: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

Q: 1. Verify whether the vector X is a solution of the given system where X; X =| 3 X' =

A: Given:

Q: Solve the following system T1 + 2x2 – 13 + 3x4 2.x1 + 4x2 – 2z + 7x4 4 10 -x1 + 2x2 + x3 – 4r4 -6…

A: We have solve given system of linear equations-

Q: Consider the system X + 3x, + 2x3 7x4 8x, = 3x, + 4x5 = -5 -x 2.x, 2.x, 8x + + 8r, 8x5 %3D - (i)…

A: To find the solution of system of consistent

Q: x1 x₁ + 3x25x3 = 4 x₁ + 4x2 - 8x3 = 7 -3x17x2 + 9x3 = -6

A: We have the set of linear equations as x1+3x2-5x3=4x1+4x2-8x3=7-3x1-7x2+9x3=-6

Q: Find the vector form of the general solution of the given linear system Ax = b; then use that result…

A: Given: x_1 +x_2 +2x_3 = 5 x_1 +x_3 = -2 2x_1}) + x_2+ 3x_3 = 3

Q: The distance of a point in the 3-D system from the origin A. is defined by the absolute value of the…

A: Given : To find the distance of a point in the 3-D system from the origin

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

Q: Consider the system of equations below x1 – 2x1 – x3 + 3x4 -2x1 + 4x2 + 5x3 - 5x4 3x1 – 6x2 – 6x3 +…

A: NOTE: Refresh your page if you can't see any equations. . write a vector equation that is equivalent…

Q: The vector (1,-2, –3) is a solution of the linear system: X1 + 3x2 - 3x3 = -2 5x1 + 13x2 - 13x3 = -8…

A: We have to solve the problem

Q: Consider the linear system Ax =b for a given constant vector b. Determine whether the following…

Q: find a homogeneous linear system of two equations in three unknowns whose equation in three unknowns…

A: For the solution of the problem follow the next step.

Q: Determine if the following linear system is consistent; if so, give a parametricvector form…

Q: Find a basis for the solution space of the following homogeneous system of equations: 0 -4 -2 2 1 -2…

Q: Give the parametric vector form of the general solution of the following system of equations: -1…

A: x1-5x2-2x3 -4x5-4x6 =-1 -x4+4x5-3x6 = 8x1-5x2 -6x5 -6x5=…

Q: 253 For the linear system AX=B, if A1=1 0 1 and B = %3D 1 2 then the unknowns vector X=

Q: Find all solutions, if any, to the linear system Y + 3z 5y + 2x -1 - 3. 3x 3y + 2z -4 Express your…

Q: I. Write down the solution set for each system with variables x, y, and z. If the solution set is…

Q: The vector (0, 2,-3) is a solution of the linear system: X+ 4x2-4x3 = 24 5x1 + 16x2 – 16x3 = 96 -…

Q: 3. Given the system dt 2 -3 - (² 3²³) * 2 (a) Find the general solution. (b) Find the solution that…

Q: 1. Consider the following system of linear equations: X1 + kx2 = 2 kæ1 + x2 + 13 = 1 x1 + x2 + x3 =…

Q: Consider the system, & use Computer algebra systems to solve systems dx/dt = 4x - 3y,…

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

Q: The vector (1,-2, –6) is a solution of the linear system: X1 + 4x2 – 4x3 = 21 5x1 + 18x2 – 18x3 = 95…

A: Explanation of the answer is as follows

Q: 16. As in Exercise 15, describe the solutions of the following system in parametric vector form, and…

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

Q: Q2. Find the basis and dimension of the solution space of the homogeneous linear system X1 – 4x2 +…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given 2 8 -2 -10 -67 [1 4 0 -4 -17 rref 1 4 -2 -6 -5 0 0 1 1 -1 -4 1 5 3 0 0 use the reduced row…

Q: Consider the following system of linear equations: 2.51c1 + 1.48x2 + 4.53x3 = 5.56 1.48x1 + 0.93.x2…

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A: The given matrix is A= 2 -3 1 2-2 0-1 1 3 2 0 4 0 -3 1-2 We have to…

Q: Find the vector form for the geveral selution to the system of equations. X, - X, + Zxg - xy - Xx=-8…

Q: Each linear system has inﬁnitely many solutions. Use parametric equations to describe its solution…

A: We will use parametric equations to describe its solution set for the given system of linear…

Q: Write the system in vector matrix form: *-3%, + 2%, - 26", x=-2%,+4x,+ sin(31), *-4x, - 3%,-21] x',…

Q: Write the solution set of the related homogeneous system, Ax = 0, in parametric form if A is row…

A: The given homogeneous system Ax→=0→ in the row equivalent form, 1-3171501-3-4

Q: Find all solutions, if any, to the given system of equations. Express your answer in vector form. y…

Q: Find all solutions, if any, to the given system of equations. Express your answer in vector form. +…

A: There are three equations and three unknown variables. x-y+2z=-2 ⋯ (1)2y-z=-4 ⋯ (2)x+y+3z=-10 ⋯ (3)

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A: Given matrix, A=3-612-12-4 Find all solution of Ax=0 in parametric vector form.

Question

Describe the solutions of the given system into parametric vector form.

x1+x2+ 2x3= 9

2x1+ 4x2−3x3= 1

3x1+ 3x2+ 6x3= 27

Also compare this solution, geometrically, with the solution set of the following homogeneous system.

x1+x2+ 2x3= 0

2x1+ 4x2−3x3= 0

3x1+ 3x2+ 6x3= 0

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1 Given

Step 2 To show

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Systems of Linear Equations$

Learn more about

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

Similar questions

Determine if the statement is true or false. If the statement is false, then correct it and make it true. It is possible for a system of two equations and two variables whose graphs are a hyperbola and an ellipse to have exactly five real ordered pair solutions.
Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.
Write the solution of the given system in parametric vector form. xi + 3x2 + x3 = 1 -4x1 – 9x2 + 2x3 = -1 -3x2 - 613: -3
determine the solution set of the linear system: x3-x4=-2 x1-x2+2x4=1 -3x1+3x2+2x3-8x4=-7 write your solution in parametric vector form.
Give the parametric vector form of the general solution of the following system of linear equations: -4x1 +x2 9. -8x1 +2x2 18 +x2 x2
Consider the system of equations below x1 – 2x1 – x3 + 3x4 - 2x1 + 4x2 + 5x3 - 5x4 - 3x1 – 6x2 – 6x3 + 8x4 2 Write a vector equation that is equivalent to the system of equations. Find the general solution of the system.
Describe the solutions of the following system in parametric vector form. Also, give a geometric description of the solution set. *1 + 3x, +x3 = 1 -4x, - 9x, + 2x, =-1 -3x, - 6x, = -1.
2. form: Solve the system of equations. Put your solutions, if there is one, in parametric X1 -X1 + X2 + X3 = 1 + X2 + 4x3 = 2 2x2 + 5x3 = 4
Determine if the system has a solution. If so, write the solution in parametric vector form. How does this compare to the solution(s) to the homogeneous linear system with the same coefficients on each variable? -x1 + X2 2x1 + 3x2 x1 + X2 - 5x3 5x3 x3 = = -1 12 5
Express the following system of linear equations as a vector equation. 9x19x2 + 6x3 = -1 3x1 + 8x2 + 0x3 1 = -2x1 + 0x2 + 6x3: 8-8-8-8 = 4
Suppose the solution set of a system of linear equations can be described as x₁ = 2-5x4 x₂ = -4x4 x3 = 5 +9x4 with 4 free. a. Write the solution to this system in parametric vector form. x = DNE x+x4
Write the solution set of the given homogeneous system in parametric form. + 2x2 + 17x3 0 12x2 97x3 0 4x2 24x3 0 x1 - 5x1