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.

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.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

See similar textbooks

Related questions

Q: 3. Determine whether the given set is a subspace of M2x2 with real entries. {6 ) la = b}.

Q: Is that Ø is balanced set O True O False

A: As per the rules we can answer only the first question and rest can be reposted.

Q: Determine whether or not the given set W is a subspace. A W = {T E R" | AT = 23 – BE }, where A, B…

Q: ? ? ? ? ? ✓ 1. V = C³ (R), and S is the subset of V consisting of those functions y satisfying the…

Q: - c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Fine the vector y by the…

A: year x 1951 13 1952 23 1953 21 1954 27 1955 37 1956 52 1957 34 1958 42 1959 31…

Q: Let V is finite vector space and suppose that V=internal direct sum of U and S1. Also V=internal…

A: Either S1 and S2 will be disjoint or identically same. If S1 is a subset of S2 then S1= S2.

Q: show thal the set of all poiuts in the Subspace of IR 3. plane ax +by+CZ =0 is +cz = ois CA

Q: The set S is {F}} 2 -2 5 neither an orthogonal set nor an orthonormal set. an orthogonal set. a…

Q: which of the following are subspaces of R3 provide typed answer

A: To determine which of the following area subspaces of R3. (A) All vectors of the form (a,0,0) (B)…

Q: 13. Which of the following is a subspace of R4? Justify your answer. a) S = {(a,b, c, d) E R* | a…

Q: Suppose W,, W2,. (a) span (W, W2 (b) If S; spans W; for i = 1,...,r, then S, US, U...US, spans W, +…

A: (a) W1+W2W1+W2 would be W2W2. Below is the justification. x+y∈W1+W2,wx+y∈W1+W2where x∈W1x∈W1 and…

Q: Let V be a 8 dimensional vector space over the set of reals. Then the dimension of a subspace of V…

Q: Determine; if W = the set of all odd functions is a subspace.

Q: The integers 1 through 36 (inclusive) are used once each as the coefficients for six vectors in P 5…

A: We know that, A subspace is a vector space that is contained within another vector space. So every…

Q: Show that H = : a, b eR is a subspace of M2x2(R). Hint: try to write H as the spa of a set of…

Q: If V is a linear subspace of R", and x1 , ×2 , ... , Xn E V, then we must have span {x1, X2, Xn} =V.…

A: To determine that the statement, if V is a linear subspace of ℝn and x1, x2,....,xn∈V, then spanx1,…

Q: an C a E R°, a+b+c=1} is a subspace of the vector space R°. The set S =- an C an C O a. True b.…

Q: Prove that the set ? = {(a + b, a -b): a and b are real numbers} is a subspace of ℝ2 with the…

Q: Which of the following sets W is NOT a subspace of R3? (Select all that apply.) O w= y : 3x-y+2z-1=0…

A: To identify the which of the given sets are not subspace.

Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B). I…

A: Given that X is a nonempty set with subsets, A, B, and C. The objective is to prove that…

Q: 15 Suppose U is a subspace of V. What is U + U?

A: Let V be a vector space and U be it's subspace. Then , for all u,v ∈ U u+v∈U and cu ∈ U ,where c…

Q: Suppose C is a linear code (i.e. subspace), and u,v are in the same coset of C. Show u+C = v+C

A: Definition A subset C⊆V(n,q) is a linear code if1) u + v ∈ C for all u, v ∈ C2) au ∈ C for all u ∈…

Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 19, Un 28 国 26 20 -2 -26…

Q: Either prove or disprove that the set V is a subspace V ⊂ R^n defined by V={x: Ax=λx}where A is…

Q: Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}

A: We want to show that U∩W≠{0}

Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: 3. This problem is about set addition and subspaces. Let d = and dz = and V = span{d}, %3D U =…

Q: All vectors and subspaces are in R". Note you only have 5 attempts for this question. Check the true…

A: The objective of the question is to identify the true statements among the given options related to…

Q: The set of all vectors in R squared that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy 3x+4y=1 is not a subspace of R squared. i.e.…

Q: suppose Vi =( 6,I,0,-1), V2 =(0,りも,1) and b= (l,2,-1,-1). iet W be spanned by v, and Vz. Find…

Q: Show that Null Space of Ax = 0 is a subspace. To get full credit you need to show that 1.0 is in the…

Q: If (a + ß)A ≤ αA + ßA then A is Subset of vector space Option 4 Option 1 Subspace

Q: S� is a set of vectors in a vector space V�, then SpanS is a subspace of V�. Please show that this…

Q: Show that every subspace of ℝ is either {0} or ℝ.

A: Given: ℝ. To Show: Every subspace of ℝ is either {0} or ℝ.

Q: Explain why the subset а —b S : a + b а,b€ R -2b — За of R³ is or is not a subspace of R³.

Q: Find the closest point to y in the subspace W spanned by V₁ and V₂ 2 4 -6 2 3 3 2 y = a. O O a O с…

Q: 6. Are the following sets subspaces of P₂? Why or why not? (a) U = {p = P₂|p(3)=0} (b) W = {ao + a₁x…

Q: Consider the following subset U= $(x,1/4, 27 1x, y, z ERG € R², is U a sector subspace of Re. show…

Q: 2. Determine whether each set described is a subspace or R2. Justify your answer. H (a) The set of…

Question

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.

Expert Solution

Step 1

Given:

H={ (x, y, z)∈ℝ³ ∣ 2x+3y-3z=4 }

To check: H is a subspace of V=ℝ³ or not.

This can be done as follows:

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
Which vector spaces are isomorphic to R6? a M2,3 b P6 c C[0,6] d M6,1 e P5 f C[3,3] g {(x1,x2,x3,0,x5,x6,x7):xiisarealnumber}
Let V be the set of all positive real numbers. Determine whether V is a vector space with the operations shown below. x+y=xyAddition cx=xcScalar multiplication If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.
Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.
The set of all vectors in R squared that satisfy 3x+4y=1 is a subspace of R squared . True False
Please show work
is a subspace of M,,3-
Please go through each option with explanation
If S� is a set of vectors in a vector space V�, then SpanS is a subspace of V�. Please show that this statement is true
If X is an inner product space, and Ais subspace of X then A = A-L True False