x [ũi |….. Jūs]. If the equation AX = 0 5 dimensional subspace of R7. nded to form a basis for R5. det(adj(B)) = (det(B))"-'.

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

A:

Q: 5. Find basis for the subspace u- of R for the vector u (1,3, -4). (Here u- means %3D orthogonal…

A:

Q: 3) Suppose TE L(V) and U1, . , Um are subspaces of V invariant under T. Prove that U, ...+ Um is…

A:

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: In the vector space of all real-valued functions, find a basis for the subspace spanned by {sin t,…

A:

Q: Find the orthogonal projection ŷ of y = onto the subspace W = Span { uị u2 5 Ex: 1.23 : ŷ =

A:

Q: 1 Q5. Find an orthonormal basis of the subspace spanned by the vectors

A: The solution is given as

Q: 2 Find the orthogonal projection of u = 1 onto the subspace of R3 spanned by the vectors -3 - 2 V1 =…

A:

Q: Use the Gram–Schmidt process to find an orthonormal basis for the subspace of R4 spanned by x1 =…

A:

Q: The set S = ( (x.y, 2) ER |2 = 2, x,y,ZER)is a subspace under vector addition and scalar…

A: This question is related to linear algebra topic vector space.

Q: Prove that the subspaces of R3 are {0}, R3 itself, and any line or plane passing through the origin.

A: Let S be a subspace for R3   Hence,              If S is the subspace then by definition:…

Q: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

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: 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: In the vector space of functions f: R → R, find a basis for the subspace spanned by {sin t, sin 2t ,…

A: Solving question by theorem vector space

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

A:

Q: at | f = a is a subspace of RI0,1] if and

A: Two step test

Q: (3) Suppose that V is a finite dimensional vector space over R and T € L(V) has no eigenvalues.…

A:

Q: if a vector space is the set of real valued continuous functions over R , then show that the set W…

A: Given V is a vector space of all continuous functions over ℝ. W is a set of differential equation…

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: Find a basis for the subspace given by the plane −3x + 2 y + 5z = 0.

A: Given that, -3x+2y+5z=0

Q: Theorem 6.14. For any a < b in R, the subspace [a, b] is compact.

A: The objective is to prove that any a≤b in ℝ the subspace a,b is compact. Let's prove the theorem by…

Q: ind the closest point in the subspace with the (not orthogonal) basis {b1, b2, b3} to the head of…

A:

Q: Let  S=span(e1),  T=span(e2) and  W=span(e1+e3) be subspaces of R3.  S is orthogonal to T, T is…

A: Orthogonal Subspace

Q: Prove that if S1 and S2 are orthogonal subspacesof Rn, then their intersection consists of only the…

A:

Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1,…

A: To find- Find an orthonormal basis for W⊥, where W is the subspace of ℝ4 spanned by the vectors -1,…

Q: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

A:

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

A:

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

A:

Q: -2 Find an orthonormal basis of the subspace spanned by the vectors 3 1310

A: Given 3 vectors. We need to find an orthogonal basis of the subspace spanned by the given vectors.…

Q: Let H be the subspace of R with basis B = 3. and let x = 10 6. Is xa vector in H? 14 fx is in H,…

A: Given H is a subspace of R3 with basis {204,231}And x=10614To check x is in H

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

A:

Q: Next Find a basis of the subspace of R° spanned by the following vectors: -1 -5 3 -4 -4 -1 2 -4 3. 7…

A:

Q: 9. Find the vector closest to y from the subspace of Rª spanned by Vị and v2. 3 1 Vị = 1 , y = V2 =…

A: To find  The vector closest to you from the subspace of R^4 spanned by v1 and v2.

Q: Let V be the subspace of C[a, b] spanned by1, ex, e−x, and let D be the differentiation operatoron…

A:

Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

A:

Q: 4. Consider C" as a real vector space. It has a subspace U := C x {0}"-1. What is the dimension of…

A:

Q: If x is in W, then x is orthogonal to some vector in a subspace W

A: SOLUTION-

Q: Find a basis for the subspace given by the plane −3x + 2y + 5z = 0.

A: we have to find a basis for the subspace given by −3x +2y + 5z = 0.

Q: If Pa is the Vector Space of poly romiels Of degee ss and Be is tho kctor of Spaco Of purynomals of…

A:

Q: Let W be the subspace of R3 with orthonormal basis {w1, w2}, where

A: Given: w1=010 w2=15025 v=12-1

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: 2. Let S = {vi, v2, V3} be a set of linearly dependent vectors in an inner product space V. What is…

A: To explain: What will be the result when we apply Gram-Schmidt process to a linearly dependent set…

Q: 4. Consider the subspace V of R' given by 1 3 V = span (a) Find an orthonormal basis for the…

A: Solution:-

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

A:

Q: The cosine space F3 contains all combinations y(x) = A cos x+ B cos 2x+C cos 3x. Find a basis for…

A: