Verify that V5 is a subspace of RS

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

Q: Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.…

A: a) Suppose that    be  a  basis  of      Then, which is  a  contradiction.    Hence, is  not a…

Q: A set of 4 vectors in R5 is linearly independent cannot span R5 spans a 4-dimensional subspace of…

A: Given a set of 4 vectors in ℝ5.

Q: Why is this set not a subspace of R^3? W = { (a1, a2, a3) : a22 = a1 - a3 } ( the two 2s are…

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Q: Which of these are linear subspaces? :2x +3y=D0}in R? :xy: A. Is a linear subspace ):v = 1– x}in R?…

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Q: Give an example of a non-zero subspace of R^4 which has dimension > 1 and does not contain any of…

A: Consider the example f(x) = {2 + x + x2}, this given polynomial has dimension 3 with the basis {1,…

Q: Find a basis of the subspace ofRª defined by the equation 7x1+9x2+ 6x3 + 5x4 = 0. Basis:

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Q: can a subspace of R^n have a dimension less than n.

A: Yes , it can be .

Q: Which of the following sets is not a subspace of the space R^3? (a) R^3. (b) Any plane passing…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: 1 0 Span 1 2 -3 N -2 -2 5 3 -2 2 9 3 I[s -2 4 0

A: The given spanning set in ℝ5is span10-12-3, -2-25-29, 0-2306, -1-2406. We have to find the dimension…

Q: Write the equation of a subspace that passes through a point a ∈ R^d and is orthogonal to a given…

A: Let d=3  Now we will find the equation of subspace that passes through a point a€R^3 and orthogonal…

Q: Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: The given vectors are                                   -3110, -12613, 3-55-6, -33-23…

Q: ( › Given 7 = 178/33 -292553/44682 321593/44682 25405/14894 4 -5 53 ال لیا , 5 2 3 -B-0 and -6 7 -36…

A:

Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W. Show that V ∩W…

A: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W.  We have to…

Q: Is S = {(x1, x2)^T ∈ R^2| x1 > x2} a subspace of R^2? Justify your answer.

A: Solution:Given: we have to check that is a subspace of or not.

Q: Find a linearly independent set of vectors that spans the same subspace of R* as that spanned by the…

A:

Q: Why isn't R2 a subspace of R³?

A: For being a subspace a space must be a subset of the other. But here R2 is not a subset of R3. So…

Q: Could you provide an example for finding a basis (of a subspace) of an orthogonal complement?

A:

Q: Discuss what it means to be a subspace and what is required to prove that something is a subspace.…

A: Concept:

Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

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Q: Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.…

A: The set forms a basis for the subspace of R3 that the vector span.Explanation:

Q: Is W=set of upper triangular 3x3 matrices a subspace of V= all 3x3 matrices? Support your answer to…

A: According to the given information, it is required to show that set of all upper triangular matrices…

Q: et aj = (1,3, –2), a2 = (5,1, 4), and b = (6, –9,3). a) Project b onto the line through aj. b)…

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Q: Let M = x2 :¤1, x2 E R X1

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Q: W = (x:x= X1 X2 LX3 where x3 = 5x₁ + 8x2

A:

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: Find a basis of the subspace of R* consisting of all vectors of the form X1 -8x1 + x2 —6х — 2х2 -6x1…

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Q: Determine whether the statement below is true or false. Justify the answer. A subset H of R" is a…

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Q: Determine all subspaces of W.

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Q: Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?

A: Given, ℝ2×2=abcd: a,b,c,d∈ℝ Let M be the set of all 2×2 noninvertible matrices  i.e.…

Q: A set S of vectors in R4 is given. Find a subset of S that forms a basis for the subspace of R4…

A: The set S of vectors in ℝ4 is given as follows. Here vectors are v1=39-99, v2=315-1516, v3=418-1819.…

Q: In linear algebra, a subspace of R^n can have a dimension less than n.  (True or False)

A: Given that the space and subspaces of the space. In general the subspace of every space have…

Q: Compute the projection of (1, 1, 1) onto the subspace generated by (0, 1, 0) and (-4, 1, 3)". Record…

A: