3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

Q: Prove thatII = {(x, y, z)|x – 2y+ 3z = 0}is a subspace of JR³, %3D -

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Q: Suppose U, W,, W, are subspaces of a vector space V. Show that (Un W,) + (UnW,)Cun (W, + W,) Find…

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Q: 5. Show that if H and H2 are two orthogonal subspaces of H, then Hin H2 = {0}. Does the converse…

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Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True False

A: Solve the following

Q: Let W - (a + bx + cx + dx'l a +b-0 and c - 3d = 0) be a subspace of Py. Then the dimension of W is…

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Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find  The closest point y in the subspace W spanned by v1 and v2.

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

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Q: 4. Assume that T E L(V) and that U1 and U2 are T-invariant subspaces of V. Prove that U1 n U2 is…

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Q: Find the orthogonal projection of 4 onto the subspace W of R* spanned by 1 1 -1 projw (7) =

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Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

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Q: 9. Find the orthogonal projection y of y = onto the subspace 2 0. W Span u = -3

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Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

Q: 10. Under the usual operations in R2, which of the following subsets is a subspace? (a) y = 2ar…

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Q: Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R

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Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…

A: To find The closest point to y in the subspace w spanned by u1 and u2

Q: Find the orthogonal projection ŷ of y: 6 onto the subspace W = Span { ui u2 Ex: 1.23 ||

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Q: Show that S = {(x, Y, z)|4x – y + 5z = 0, x, y, z E R} is a subspace of R³.

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Q: For a certain subspace W, the orthogonal projection of the vector y = 3 onto W is ŷ 2. Use this…

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

A: To Prove U is a subspace of vector space V 1) 0∈U  If x, y∈U  and a∈V  2) Closed under vector…

Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

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Q: What is the dimension of the subspace W = {A = [aij] € R4x5|a45 = 0} dimW = Ex: 5

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Q: [5 Find the orthogonal projection ŷ of y = onto the subspace 3 W = Span { uį = 2 u2 3 Ex: 1.23 ŷ =

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Q: the set B=E[f る,L 2 ), L3 10 in M22 the subspace of Mez spanned by B. Since carly independent Cyou…

A: Note: As per bartleby's  guideline for more than one question asked only first is to be answered…

Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: If Sz is a subspace of R" of dimension 3, then there cannot exist a subspace S, of R* such that Si c…

A: This staement is true.

Q: Let W = {a + bx + cx² + dx³| c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to

A: As given W be a subspace of P3.

Q: 4. Let S be the subspace of P₂ defined by S = span{1-x, 1+x, 5, 1-x², 2x}. Find dim (S), and show…

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Q: Suppose that X = ER' :z + y + z = 0 and ² + y² = z² Determine (with justification) whether X is a…

A: Given  X=xyz∈ℝ3:x+y+z=0 and x2+y2=z2

Q: Let S1 = {(xy)/ x22y-1}, S2 = {(x,y)/x <3, 1s y 5} and S3 = {(x,y)/ O< x<3, 1sys5}. %3D Then: S1 and…

A: We use the result  compact subset of R is closed and bounded.

Q: 2. Is the set of vectors of the form a b a+2b a subspace of R³? Show your proof.

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Q: If y is in a subspace W, then y - ŷ is not zero. Select one: O True O False

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Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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Q: Show that [0, 1] and (0, 1] as subspaces of R with the usual topology are not homeomorphic.

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Q: Let W = (a + bx + cx2 + dx'| c- 3d = 0} be a subspace of P. Then the dimension of W is equal to O…

A: dim(W) = number of vector in the basis of W.

Q: Suppose that U cr|xyer F4 y EF, U is a subspace of F4- you don't have to! Find a subspace V of F4…

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Q: Find the orthogonal projection ŷ of y = 6 onto the subspace 2 -3 W = Span { ui = 3 Ex: 1.23

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Q: 4) Find all values of h such that Y will be in the subspace of 3. R spanned by VI) V2, V3 if V I V2…

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = eܐ ܝܕ ܝܐ [19 12 1…

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Q: Show that [0,1] and (0,1] as subspaces of R with the usual topology are not homeomorphic.

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Q: Consider X = {1, 2, 3, 4, 5} where the topology is {U C X|1 E U}. Find a subspace of X which is…

A: Consider the set X = {1,2,3,4,5} where the topology is {U ≤ X : 1 ∈U}. We have to find a subspace of…

Q: 4. Let S be the subspace of P2 defined by S = span{1-x, 1+x, 5, 1-x², 2x}. Find dim(S), and show how…

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Q: 1- Show whether the set of polynomials a, +at +at+at ,where a, =a, +a, is a subspace of P3 or not ?

A: Let V be a vector space over the field F. A non-empty subset S of the vector space V is said to be a…

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: Let W {a + bx + cx2 + dx³| a+b = 0 and c- 3d = 0} be a subspace of P3. %3D Then the dimension of W…

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Q: If y is not in a subspace W, then y-y is zero. Select one: O True O False

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Q: Consider the subspace Wof D, given by W = span (cos x, sin x, x cos x, x sin x). (a) Find the matrix…

A: f(x) = cos x + 2x cos x

Q: For a certain subspace W, the orthogonal projection of the vector y = 5 onto W 4 is ŷ = |1. Use this…

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Q: 4. Find the distance from the vector j = to the subspace on R³ spanned by { 19: | }

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Q: Show that points on the plane x-2y+4z=0 form a subspace of R3

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Q: Find the closest point to y in the subspace W spanned by v1 and v2 2 1 y = -2 -3] 1 2 а) b) 2 c) 1…

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