For which value of a is the solution set of the following system x + 5y + z = b − 5 2x − 4y − z = a + b − 3a subspace of R^3? 5 For which value of a is the solution set of the following systemx+ 5y + z = b – 52х — 4у — z 3D а +b-3a subspace of R³?

Consider the given equation. x+5y+z=b-52x-4y-z=a+b-3 Since, the given have three variable and the…

Answered: For which value of a is the solution…

For which value of a is the solution set of the following system x + 5y + z = b − 5 2x − 4y − z = a + b − 3 a subspace of R^3?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

See similar textbooks

Related questions

Q: Assume that the vectors sint cost X2= sint - cost , and X,= sint +cost sint -cost 0. sint +cost are…

Q: Chapter 6, Section 6.2, Question 019 Find the valume of the sold whose base is the region bounded…

A: The given curve is, y=x3

Q: Find the dimensions of the rectangular box of maximum volume that has three of its faces in the…

A: Let say that(a,b,c) is point in plane 4x+3y+z=12 and it is one vertex of requested rectanglar box.…

Q: What must be value of X so that B is diagonalizable?

A: A matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such…

Q: A tank was modeled in a pyramid shape of heght 4 using four different planes -4/3x-4y+z=-4 ,…

A: Consider the equations of given four different planes, -43x-4y+z=-42x-4y+z=-42x+y+z=-4-43x+y+z=-4…

Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

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

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Apply Jacobi's or Gauss Seidel method to the given system. Take the zero vector as the initial…

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: Verify whether the vector X is a solution of the given system where 2. X' X; X: %3D 1 0

A: The given differential equation is X'=2110X. Note that, X=13 et+4-4…

Q: A rectangular field of fixed area is to be enclosed and divided into three lots by parallel to one…

A: Given: A rectangular field of the fixed area is to be enclosed and divided into three lots parallel…

Q: Explain the term Vectors that Span a Subspace.

Q: I want to convert z=x2−2xy+1 to tensor product blossom and compute the control points if its over…

Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: Apply Jacobis method to the given system. Take the zero vector as the initial approximation and work…

A: Given : 4.5 x1 - 0.5x2 = 1 ...(1)x1 - 3.5x2 = -1 ...(2)

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: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

Q: Show that the vector of residuals and the vector of fitted values are orthogonal. Also, show…

Q: Hex reasoned that a moving point traces out a line segment, and that a line segment moving parallel…

Q: Find all critical points of the given plane autonomous system. (Order your answers from x' = -x(4-…

Q: Maximize 4x+ 2 y+ 2 z

A: We have to maximize f(x,y,z)=4x+2y+2z on the sphere x2+y2+z2=19.Take g(x,y,z)= x2+y2+z2-19=0Thus,…

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

Q: Express the product Ax as a linear combination of the column vectors of A. 2 3][3 -4 + 2 3 5 + 3 |…

A: To find out the correct option.

Q: Based on the graph, give an example of linear combination that will result in a zero vector (weights…

Q: Q6. Classify critical points of the given plane autonomous system and sketch some trajectories on…

A: Q6. The given equations are,x'=-3x+y2+2y'=x2-y2

Q: 2. Can there be flow across a streamline? Why?

A: There is no flow across a streamline.

Q: 9. Explain why four vectors is R³ are always linearly dependent.

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

Q: Apply Gram- Schmidt process to the vectors 3

Q: By separating the variables convert the PDE into a system of ODES U = U x PLEASE HELP

Q: Verify that the vector X is a solution of the given homogeneous system. -1 X' = 4 X; x = -3t/2 1 (*)…

A: Given the homogeneous system is x'=-1141-1x x=-12e-3t2

Q: Consider the set of points (x,y) in the xy-plane 1 3 4 y 3.1 3.8 4.1 2.9 1.6 Find the least squares…

A: Least square solution of the coefficient are the same of solution of Normal equation.

Q: Give the family of orthogonal trajectories for the equation: y2 = Cx5+5

A: To obtain the family of orthogonal trajectories for the equation: y2 = Cx5+5. Find a differential…

Q: What will happen if the Gram–Schmidt process is applied to a set of vectors {v1, v2, v3}, where v1…

Q: In February 2008, Speedo released its new LZR Racer swimsuit made of polyurethane and woven elastane…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: what are the independent and dependent variables of this problem? is the DE separable?

Q: Determine the minimum point of fx) =x,²+x,x, +x,² – 3x, – 3x, by using conjugate gradient method,…

Q: Find the family of orthogonal trajectories of the system of circles which pass through the origin…

A: To find The family of orthogonal trajectories of the system of circles which passes through the…

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: GIVEN: y = 9 x2 x = 0 x = 1 y = 0

Q: What is the equation of the orthogonal trajectories of 4x + 5y = C? (1) 4x + 5y = k (2) 4х — 5у 3Dk…

Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: Given: The region bounded by y=2x2, x=0, x=2 and y=0.

Q: Explain theorem of General Solutions of Homogeneous Systems?

A: General solutions to homogenous linear differential equation: Let I be an open interval, and…

Q: Subspace of IR" is 3, True faulse I or

A: Here given set V=xyz∈ℝ3: x-2=y+1=z

Q: Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Consider the regression model Y; = B1X11 + B2X2¡ + uj for i = 1,..., n. %3D • Specify the least…

A: Given- Consider the following regression model Y₁ =B₁X₁₁ + B₂X21+U₂ for i=1,2,...,n Consider the…

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

100%

For which value of a is the solution set of the following system
x + 5y + z = b − 5
2x − 4y − z = a + b − 3

a subspace of R^3?

5 For which value of a is the solution set of the following system
x+ 5y + z = b – 5
2х — 4у — z 3D а +b-3
a subspace of R³?

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

Learn more about

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

Similar questions

Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
the subset H={(x,y,z)∈ℝ³∣ 2x+3y-3z=4} it can be assured: * if u ∈H, v∈H , then u⊕v∈H* if u∈H, then c⊙u∈H, for all c∈R * H is a subspace of V=ℝ³ answer in each one if it is: False, true or cannot be established.
let S be the collection of vectors [x] (2x1 matrix )in R2 that satisfy the given [y] property. In each case, either prove that S forms a subspace of R2 or give a counterexample to show that it does not y=2x
The set of all vectors in R squared that satisfy 3x+4y=1 is a subspace of R squared . True False
if v is in R3, does the set of vectors x with v x x=0 is a subspace?
Which of the following are vector subspaces of R4? all vectors of the form (a, b, c), where b = a + c? all vectors of the form (a, b, c), where b = a + c + 1? Note: In the image the problem is described more clearly, do not skip any step and solve the two parts a and b.
let S be the collection of vector [x] (3x1 matrix) in R3 that satisfy the given [y] [z] property. In each case, either prove that S forms a subspace of R3 or give a counterexample to show it does not. z=2x,y=0
Show that (a,b,c) where c=a+b is subspace of R3
The vector b is in the subspace spanned by the columns of A when __ has a solution. The vector c is in the row space of A when __ has a solution. True or false: If the zero vector is in the row space, the rows are dependent.
Suppose S consists of all points in R2 that are on the x-axis or the y-axis (or both). (S is called the union of the two axes.) Is S a subspace of R2? Why or why not?
Show {s,t,4s-3t)|s and t are in ℝ} is a subspace of ℝ3.