Answered: Determine whether the subset W below is…

Determine whether the subset W below is a subspace of R³ with the standard operations Justify your answer. W = { (s, t, s+t)|s and t are real numbers}

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

See similar textbooks

Related questions

Q: Determine whether the set S spans R2. If the set does not span R2, then give a geometric description…

Q: Let W = {a + bx + cx2| a+b >1} with the standard operations in P2. Which of the following statements…

A: Given set is

Q: Consider the subset S {(a, b, c) : abc 0} of R3. Give 3 examples of elements in this sub- set Then…

Q: Which of the following is a subspace of R2 with the standard aperations A. W- 0x); x are real…

A: A non- empty subset W of a vector space V over a field F is said to be a subspace of V if and only…

Q: Let W = {A = E Mai A = ) with the standard operations in Ma3- Which of the following statements is…

Q: Determine whether the set W is a subspace of R with the standard operations. If not, state why.…

Q: (iv) T cannot be a subspace of V. Justify your answer. True or false: If T is a proper subset of V…

Q: Determine whether the set W is a subspace of R3 with the standard operations. If not, state why.…

A: The given vector space is R3.And the set W is given byW=x1,x2,8:x1 and x2 are real numbers.We need…

Q: 2. Determine whether W = {a + br + cr?; a, b, c € R, a · b.c= 0} is a subspace of P2.

Q: 12. Which of the following subsets of R² are subspaces? Give a geometric interpretation whenever…

Q: In the subsets below, check which of them are vector subspaces of R³ relative to the usual…

Q: Let R[x] be the set of polynomials in x with real coefficients. Define the subset V = {p(x) E R[a] |…

A: This question from linear algebra.

Q: (b) Let V be R² with the standard definitions of addition and scalar multiplication. - Let W = =…

Q: Determine whether S={a, +a,x+a,x :a, +a, +a, = 0} is a subspace of P.

A: Here S is a subspace of P2

Q: Determine if the subset of C(- o, co) is a subspace of C(- co, c0). The set of all nonnegative…

Q: Determine whether W = {(a,2,b)|a,b ∈ R} is a subspace of R^3.

Q: Determine whether the following subset W = {(a, b, c)| a + 2b = c} is a subspace of V = R^3 or not?…

A: A subset W of a vector space V is said to be a subspace of V if, for all vectors u,v∈W and scalar k…

Q: Determine whether the set S spans R2. If the set does not span R2, then give a geometric description…

Q: Let W = {(x1,x2, X3)| 3x1 x2 = 0}with the standard operations in R3. Which of the following…

Q: The following subset of R W ((a,b.c): a +b+c 0} is a subspace of R'.

A: Subset of R2 is given W=(a,b,c):a+b+c=0W is subspace if and only if α,β∈W and c∈F(field)⇒cα+β∈Wlet…

Q: Determine whether the set W is a subspace of R3 with the standard operations. Justify your answer.W…

Q: 7. Let W span{x} be a subspace of P2(R) with (p(x), q(x)) = p(x)q(x) dx. Find W-.

A: I am solving this in step 2

Q: Let P3(x) = {ax3 + bx2 + cx +d |a,b,c,d in R} be the set of polynomials of degree 3 or less with…

Q: Which of the following subsets of P2 are subspaces of P2? Explain your answer. If it is a subspace,…

A: A detailed solution is given below.

Q: Determine whether the set W is a subspace of R3 with the standard operations. If not, state why.…

A: The given set needs to be a subspace of R3 if all the elements in it belong to R3 and they obey all…

Q: For each subset W of R² either prove W is a subspace of R² or explain why it is not a subspace. (a)…

Q: Show that S is a subspace of R2 where S = {x € R²: x=(5k, 10k), k = R}.

A: Given S = x∈ℝ2 : x=5k, 10k, k∈ℝ. We have to show that S is a subspace of ℝ2.

Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

Q: 5. Let H = {(a - 3b, b-a, a, b): a, b E R}. Show that H is a subspace of R¹.

Q: 3. Determine whether the set W = {(0,x2, 3, x4) : where x2 and x4 are real numbers} is a subspace of…

A: Subspace of a vector space

Q: 2) Let W1, W2 be subspaces of V. Prove that W1 UW2 is a subspace if and only if W1 C W2 or W2 C W1.

A: Let W1,W2 be subspaces of V. To prove W1∪W2 is a subspace if and only if W1⊆W2 or W2⊆W1

Q: Let M = x2 :¤1, x2 E R X1

Q: a Let W ||a,beR}be a subset of V = R², then W is a subspace of V

A: we have to show that given space is subspace of V

Q: Determine whether the set W is a subspace of R³ with the standard operations. If not, state why.…

Q: 1. Determine whether the given subset SCR² is a subspace of R? or not. (If so, prove it. If not,…

A: Here R^2 is a vector space over the scalar field R,

Q: Determine whether the set W is a subspace of R³ with the standard operations. If not, state why.…

A: The solution is given as

Q: 3. Consider V = {a2x² +a1x + ao € P2(R) : a2 + a1 + ao = 0} . Use the subspace theorem to show that…

Q: Determine whether the set W is a subspace of R3 with the standard operations. If not, state why.…

Q: Let W = {a + bx + cx²| 2a + c> 3} with the standard operations in P. Which of the following…

A: Consider W={a+bx+cx2| 2a+c>3}with operations as same as P2We check whether p(x)=0∈WLet…

Q: Let P2 be the space of polynomials of degree at most 2. Determine if the following set is a subspace…

Q: Determine whether the set W is a subspace of R3 with the standard operations. If not, state why.…

A: We have to find out the subspace

Q: Determine whether each subset is a subspace of R2.a. The set of points on the line x + 2y = 0b. The…

A: a) The set of points on the line x+2y=0 For a subset to be a subspace it has follow certain…

Q: Determine whether the set W is a subspace of R3 with the standard operations. w = {(x1, 0, x3): X1…

Q: Let P2 be the space of polynomials of degree at most subspace of P2. All p(t) € P2 such that p(1) ·…

Q: Find all values of h such that y will be in the subspace of R³ spanned 3] by v1, V2, V3 if v1 =| 2|,…

Q: Determine whether the set W is a subspace of R3 with the standard operations. If not, state why.…

A: We need to determine if W is subspace or not.

Q: which of the following sets are subspace of R'and which are not, if yes prove it, if no give an…

Q: Determine whether the subset of C(−∞, ∞) is a subspace of C(−∞, ∞) with the standard operations.…

A: An exponential function is a mathematical function in the form of f(x)=ax, where a is a constant and…

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

Determine whether the subset W below is a subspace of R' with the standard operations
Justify your answer.
W = { (s, t, s+t)|s and t are real numbers}
For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
BI U S
Paragraph
Arial
14px
A
Ix
由用区
+)
!!!

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 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

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
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.
Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.
Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
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.
In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In each case either prove that S forms a subspace of 2 or give a counterexample to show that it does not. xy0