Consider the following subspaces of R3: U = span {(1,1,0,-1), (1,2,3,0), (2,3,3,-1)}, W = span {(1,2,2,-2), (2,3,2,-3), (1,3,4,-3)}. Accordingly, find the; i) U+W subspace dimension (dim(U+W)), ii) U∩W subspace dimension (dim(U∩W)).

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

A: P2 is the vector space of all polynomials of degree 2 or less, and  H is the subspace spanned by…

Q: ts) Is W=set of upper triangular 3 x 3 matrices a subspace of V=all 3 x 3 matrices? Support your…

A: If the upper triangular n*n matrix is closed under addition and scalar multiplication then it is a…

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

A:

Q: Is R? a subspace of the complex vector space C²2?

A:

Q: 4. Determine whether the sets span R' for part a and R' for part b. If the set does not span R? for…

A:

Q: Put bases for the subspaces V and W into the columns of matrices V and W. Explain why the test for…

A:

Q: (1,-4,-2,1), (1,-3,-1,2) and (3,-8,-2,7) vectors are Spanning W space and W space is Subspace of R4.…

A:

Q: (() 2 6. Are the two subspaces span and span (() orthogonal? Justify your answer.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 0,−1), (2,1,0), (3,1,-1), (1,1,1)} spans. {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly R³. y, z) €…

A: Let us consider the set S=1,0,-1,(2,1,0),(3,1,-1),(1,1,1) To check R3=span S that is to check,…

Q: Let W { (а, b, а + 2b + с, 2а — Зc), а, ь, с€ R} %3D - 1. Show that W is a subspace of R4. 2.…

A:

Q: Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1} a subspace of R*? Show the details of %3D your…

A:

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

A:

Q: Find a basis for the subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]). Show your work, and…

A: We find basis of subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]).

Q: Find the distance from the point x = (1, 3, -2) of R3 to the subspace W consisting of all vectors of…

A:

Q: Find a basis for sunspaces of R4  a)the vector for which is x1=2x4 b)the  subspace spanned by…

A:

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

A:

Q: Find a linearly independent set of vectors that spans the same subspace of R* 4 as that spanned by…

A:

Q: Show that the set of vectors {(−4, 1, 3), (5, 1, 6), (6, 0, 2)} does not span R3, but that it does…

A:

Q: 4. The two parts of this question are unrelated. (a) Consider the set of matrices of the form where…

A:

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: Find a basis for the subspace of R" spanned by the vectors 1 1 .2. -3. .6.

A: Use the given vectors.

Q: 2. Let W be the set of all vectors in R? whose first component is 2. Is W a subspace of R2? Justify…

A: It is not a subspace.

Q: A. W = {(x1,0,1)| x, is a real number} under the standard operations in R°is a subspace of R³. B. W…

A:

Q: The set { n > 1} is closed in (0, 0) as a subspace of R. - True - False I know the answer is true…

A: Given set  1nn≥1

Q: What is the dimension of the subspace H of R? spanned by 2 -4 4 32- :? -5 10 -10 O A) 0 O B) 3 O ) 4…

A: The number of vectors in a basis of a vector space is said to be the dimension of that vector space…

Q: {] Find a basis for the subspace U = | a, b, c € R } of R³. Please justify your answer. -6

A:

Q: (R, Ts) is a topological space and NC R , find the T. subspace topology.(T|N is the subspace…

A: Let ℝ, τs is a topological space and ℕ⊆ℝ Define τs|ℕ=ℕ∩A: A∈τs Then τs|ℕ is a topology on ℕ  (i) As…

Q: 2, Find bases for the fundamental subspaces; R(A), R(A"), N(A), and N(A"), given the matrix 1 -2 2 A…

A:

Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

A:

Q: a b Show that W |a,b ER} is a subspace of M2x2. %3D -b a

A:

Q: Suppose W is a subspace of Rn spanned by n nonzero orthogonal vectors. Explain why W = Rn.

A:

Q: Let W be the subspace of R spanned by v = (1,2,1,1), v2 = (2,2,2,1) and V3= (1,0,1,0). Then the…

A:

Q: Let A = {(1, –2,0), (0,0, 1), (-1, 2,0)}. Determine if A spans R. If A does not span R°, give a…

A: To find wheather A spans R3 we have to check if it forms a basis in R3

Q: Find a basis for the subspace W of Rª orthogonal to {(1, –2,3, 4), (3, –5, 7,8)}.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 12. Let A be a fixed n x n matrix and let S = {B e Mnxn|AB = BA}. Is S a subspace of Mnxn?

A:

Q: The set of all points in R3 satisfying x + y - z = 0 is a subspace. Note that the set of point…

A: It is known that any subspace of ℝ3 should contain an additivities identity element 0, 0, 0.

Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

Q: Question: Is the subset P(x,y,z) described by 8x-y+2z=0  a subspace of R3? Why or why not?   Is…

A: Discussion is below .

Q: U = {(a,−a,b,c) | a,b,c ∈ ? } and W = {(p,q,-p,r) | p,q,r ∈ ? }. Is U ∩ W = {0}? If it isn't, then…

A:

Q: (i) Consider 3= {(a, B.Y.6):8 = 2a – B and y = a}. Is a subspace for the vector space R with respect…

A:

Q: If X = {a, b, c} and 1 = {X, 4, {a}}. Then the subspace topo log y on A = {b} is {Ø, {a, b}} {Ø,…

A:

Q: Find the orthogonal projection ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

A:

Q: 3.4. Find the distance from a vector (2,3, 1)" to the subspace spanned by the vectors (1, 2, 3)",…

A:

Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

A:

Q: I am having troubles understanding intersection of subspaces. For instance, I have these two…

A:

Q: Let W be the subspace of R5 orthogonal to u1=(1, 3, -2, 1, 1) and u2=(0, 1, 1, -1, 0), u3=(0, 0, -2,…

A: 1.Let W be the subspace of R5 which is orthogonal to S=1,3,-2,1,1,0,1,1,-1,0,(0,0,-2,1,2)…

Q: wont voy work QUESTION #10 CONTINUED b. Is the set of matrices of the form (a) a subspace of M22?

A:

Q: 1. W is the set of all 2x2 matrices of the form 0 a where a and b are real numbers. Does W 3 b form…

A: Given, W is the set of all 2×2 matrices of the form 0a3b, where a and b are real numbers. To…

Q: da basis of the subspace of IR* defined by the equation 5x1 + 9x2 + 8x3 + 6x4 = 0.

A: Explanation of the solution is given below...

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.