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 %3D V3 and y= 3. 3.

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

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

A:

Q: What is the dimension of the subspace H of R spanned by the given ved V1, V2 and v3 2 3 Vị = -8 V2 =…

A:

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: Show that the solution set to a system of equations of the form a + a, x = 0 + an x = 0 a m, + ... +…

A:

Q: Find the orthogonal projection of u on the subspace of R³ spanned by the vectors v₁ and v₂. u = (1,…

A:

Q: Find the orthogonal projection ŷ of the vector y = onto the subspace W = -7 Span u =

A:

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

A:

Q: If u and v are vectors in R and W is a subspace of R with (u - v) belong to W, then both u and v…

A: If u and v are vectors in R3 and W is a subspace of R3 with (u-v) belong to W, then both u and v…

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

A:

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 ||

A:

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

A:

Q: Let S be the subspace of Rn spanned by the vectors x1, x2, . . . , xk. Show that y ∈ S⊥ if and only…

A:

Q: to the subspace W = Span{u1, u2} where 0. Find the distance from the vector y and u2 = -2 O 2 01

A:

Q: Find the orthogonal projection of the vector v onto the subspace S. v = |2 S =

A: projS(V) = (u1.v/u1.u1)u1 + (u2.v/u2.u2)u2

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

A:

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: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

A:

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

A:

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

A:

Q: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

A: Given that a) W=x,y,z|x,y,z∈ℝ,x=z+2 of ℝ3. b) W=pt-tq of M22 Check the space W is the subspace of…

Q: Find the distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||

A: The given vector is y=-1-510 and the subspace is u=-200, v=12-1.

Q: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

A:

Q: Is T = {(x,y,z)| x+2 y+3z=0} a subspace of R?

A: Subspace

Q: Find the closest point to y in the subspace W spanned by vị and vz 2 y =| 1 ,v1 0,v2 -2 2 а) b) c)…

A: The following is the solved answer.

Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: Find the projection of the vector v onto the subspace S.

A:

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

A:

Q: Q. Show that (a,b,c) where c=a+b is subspace of R

A:

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

A: Consider the given set. U=x,-x|xinR Let, consider that, f,g∈V And f, and g is defined as.…

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

A:

Q: Find the orthogonal projection of V = onto the subspace W of R' spanned by U1 = , U2 Uz = VW ||

A:

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

Q: Find the closest point to y in the subspace W spanned by u, and u2. 7 2 y = 21 u1 2 , u2* 3 38 - 1 4…

A: Given that     y = (7,21,38) , u1 = (2,2,-1) and u2 = (-1,3,4) Here we have to find the closest…

Q: Let U and W be subspaces of R³ for which dimU=1, dimW=2, and UgW. Show that R=UOW.

A: I have shown all the conditions of direct sum of two subspaces

Q: (A) Let U1, U2, U3 be subspaces of M2x2(R). If V = U1 e U2 e U3, then dim V = 4.

A: So,  V is the direct sum of the subspaces U1, U2, U3  of M2×2(R) , i.e. dim(U1) = dim(U2) = dim(U3)…

Q: Find the orthogonal projection ŷ of the vector y = onto the subspace W = Span u 2 Ex: 5 C ŷ = %3D

A:

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

A:

Q: Find the orthogonal projection ŷ of y = 3 onto the subspace W = Span { u1 = , U2 = 3 Ex: 1.23 %3D

A:

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

A: If y is in subspace W, then the orthogonal projection of y onto W (y') is y itself.  And in that…

Q: Find the projection of the vector v = [1 0 −2]T onto the subspace

A: We have to find the projection of the vector v=10-2 onto the subspace S=Span0-11,011

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

A:

Q: i) Let V = M2x2(R) and %3D W; = {(: :) ev:a.hceR} and W2 = {(". :) ev :a,be R Prove that W1 and W2…

A:

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

A:

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…

A:

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

A: Given:   v = 123 , u1 = 2-21 , u2 = -114    Also, given that the subspace W is spanned by the…

Q: Q2. Check if the following points lies on the subspace U spanned by the vectors = [2 -1 2]', x2 = [0…

A:

Q: Find the closest point to y in the subspace W spanned by vị and vz 2 1 y =| 1 |,v1 =| 0 [0] 2 lo] 2…

A:

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.