Let 3 -13 3 3 and let W the subspace of IR spanned by ū and v. Find a basis of W, the orthogonal complement of W in R“. ||

Q: (c) Use the Gram-Schmidt orthogonalization process to find an orthogonal basis and an orthonormal…

A: We have to find orthogonal bases and orthonormal basis.

Q: 2. Let S be the subspace of R5 spanned by x = (1, , (a) Find a basis for S- (b) Give a geometrical…

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

A: vector subspace  V  of  ℝ4  given by ,               V = span 1001 , 31-11 (.)  If  W be a subspace…

Q: 1)Let W CR³ be the subspace generated by the vectors (1, 0, 1)and(1, 1, 0). a )Find the orthogonal…

A: Given W⊂R3 be the subspace generated by the vectors (1,0,1) and (1,1,0). Solution a: Since every…

Q: Let -2.5 * = -4 and j = 7 -6 Use the Gram-Schmidt process to determine an orthonormal basis for the…

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Q: The set B=(v= (1,1,1),u=(0,0, - 3),w=(2,2,0)) IS: OA Linearly independent in R3. OBa subspaces of R.…

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Q: 2) Let W be a subspace of V = Rª with basis 1 1 1 V,ミ V3 1 Using Gram Schmidt process, find the…

A: The vector of the sub-space are,

Q: 2. Let H be the set of all vectors of the form (a – 3b, b – a, a, b) where a and b are arbitrary…

A: Let V be a vector space. H is said to be a subspace of V. If  H is a subset of V. H is closed with…

Q: Is the set of all vectors of the formb, where a, b, and c are any real numbers with a +b+c > 0, a…

A: A subset W of Rn is a subspace of Rn if it satisfies Non-emptiness:  The zero vector is in W.…

Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: Let S be a subspace of R with basis B={[0,1,-3], [3,3,0]) The coordinate vector of v=[-15,-20,15]…

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Q: Let W be the subspace of vectors in R3 that are orthogonal to w = (-1, 1, 1).  Find a basis for W.…

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Q: Let -1 2 4 and let W the subspace of R spanned by i and v. Find a basis of W-, the orthogonal…

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Q: 7 4. 3 and let W the subspace of IR spanned by u and v. Find a basis of W, the orthogonal complement…

A: The objective is to find orthogonal complement of W

Q: . Is the set of all vectors of the form b where a, b, and c are any real numbers with a +b+c> 0, a…

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W-. 1 -1 1 W1 W2 -5 -2 1

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Q: 5. Let U, W be subspaces of a vector space V such that (v, ) is a basis for U and (v2, es, 4) is a…

A: We shall use the formula dim(U+W)= dim U + dim W - dim (U \cap W) to solve this problem. The detail…

Q: Find an orthogonal basis for the subspace H of IR that is spanned by the vectors 1 1 1 -2 1 V1 = V2…

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Q: 4. Let S be the subspace of R4 spanned by x = (1,0,-2,1)7 and x2 = (0,1,3, -2)T. Find a basis for S

A: Consider a matrix A as follows.

Q: Let W {(a, b, c, d)| a – 5 b = 0 } be a subspace of R*. Then a basis for W is

A: The given subspace of R4 is W={ ( a , b  ,c , d ) | a - 5 b = 0 } Let x=( a, b , c , d ) be in W…

Q: 0-0- Let ui = u2 = and set W = {w e Rª : w · v1 = w · v2 = 0}. W is a subspace of R4. Find a basis…

A: Find the dimension first and find vectors which satisfies given two relation

Q: Let -4 Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R4 spanned…

A: Given, x→=22-40,       y→=-5-101,           z→=-57-2-3 Gram-Schmidt method: Let {x,y,z} be any set…

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…

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Q: 3. Let W C R be an inner product subspace with standard dot product. { 12 then If W I1- 2r2 + 4 = I3…

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Q: Let H span {(-11,0, –5), (–3,0, –1), (–2,0, –1)}. A basis for the subspace H C R³ is { vector

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Q: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for…

A: The given question is related Gram-Schmidt process. Given that 1-101 , 6-8-31 is a basis for a…

Q: Let W = {(a, b,c,d)| 5a - b = 0} bẻ a subspace of R'. Then a basis for W is %3D ((1,5,0,0)} O…

A: option b is correct answer . below is the explanation

Q: Let W be the subspace spanned by the given vectors. Find a basis for W⊥

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Q: Let 3 ГО.5 and j = |-4 [0.5] Use the Gram-Schmidt process to determine an orthonormal basis for the…

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Q: a Let W ER a + b+ c = 0 Prove that W is a subspace of R Find a basis for W and state the dimension…

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Q: Let 5 Find a basis of the subspace of R4 consisting of all vectors perpendicular to v.

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Q: Find bases for the four fundamental subspaces of the matrix A. 189 A = 0 30 N(A)-basis N(AT) = %3D…

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Q: Let 3 -7 ,V = u -3 -3 4 and let W the subspace of R* spanned by u and v. Find a basis of w', the…

A: The given vectors are u=3-73-3, v=-12-34 and W be the subspace of R4 spanned by u and v.

Q: Let H be the set of all vectors of the form (a – 3b, b – a, a, b) where a and b are arbitrary…

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Q: 4. (a) Let {b,, b2, b3, bą} be an orthonormal basis for a three-dimensional subspace of Rº, and let…

A: For (a), Note that {b1, b2, b3, b4 } be an orthonormal basis. We are given that u = b1-2b2+b3-2b4…

Q: Let S be the subspace of M2(R) consisting of all symmetric matrices (i.e. A=AT). Determine a basis…

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Q: 5. Let S = {x + 1,x2 – 2, x – 1,3}. Find a basis for the subspace W that is spanned by S.

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Q: Find a basis for the subspace of R W- (*,X,X3, X4, X )x + 2xz + Xg = 0) {(1.0.00.1).(.-1.0.0.2).…

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Q: 2 Let A = | -4 2 Define U = {M E M2x2 such that MA = 0}. Prove that U is a subspace of M2x2. Find a…

A: We will find out the required solution.

Q: 1. Let W be the subspace of R' spanned by wi = (1, –1,0,5) and w2 = its orthogonal complement W1.…

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Q: 34. Let W be a subspace spanned by u₁ = (1, 1, 1) and u₂ = (-2, 5, -3). Write vector.orthogonal to…

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Q: Let H={p € P3: p(0)=p(1)%3D0} be a subspace of P3. Show that 8 = {-2+2t, - is basis for H using…

A: Given: H={p∈ℙ3:p(0)=p(1)=0} is a subspace of ℙ3 B={-2t2+2t,t3-t} To show that B is a basis for H…

Q: Let be a basis for a subspace of R2, 12 the Gram-Schmidt process to find an orthogonal pasis under…

A: Gram-Schmidt orthogonalization process: Given a basis U1, U2, U3 to a vector space V,  Gram-Schmidt…

Q: Let W be the subspace spanned by the given vectors. Find a basis for Wt. W = W2 = -5

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Q: a . Is the set of all vectors of the form b, where a and b are any real numbers, a subspace W of R?…

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Q: Let 9. 2 H = span 10 A basis for the subspace H C R* is { }. vector

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Q: ) Let W C R³ be a subspace with basis {{} 3 -5 -1 1 Use Gram-Schmidt process to produce an…

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Q: Let H span {(-13, –1, -3),{-9,2, –2), (-1, –5, 0)}. A basis for the subspace H C R³ is { }. vector…

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Q: 5. Let W be the set of all vectors p(t) in P such that p(0) = 0. Show that W is a subspace of P and…

A: W be the set of all vectors p(t) in P2 such that p(0)=0.

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.