1 3 1 Let vị = 1 and j = 1 |4 Let W be the subspace spannd 5 1 -1 6 by the us. Write j as the sum of a vector in W and a vector othogonal to W.

Q: Let W be the set of vectors of the form a b A = where a, b, c are real numbers such C that 8b + 3a…

A:

Q: The subspace of R spanned by the vectors ui = plane passing through the origin. Express w = where wi…

A: Let W be subspace of ℝ3 spanned by the vectors u1=45,0,-35 and u2=0,1,0. Let A=x,y,z be a non zero…

Q: Find the projection of the vector v onto the subspace S. S = span projs v= 0 -1 11 O

A: We have to find the projection of the vector v onto the subspace SWhereS = span   and v = Let v1 =…

Q: Let S={,,,} a Decide whether or not the vector b= is a member of Span(S). !f b is indeed a member of…

A:

Q: an C a E R°, a+b+c=1} is a subspace of the vector space R°. The set S =- an C an C O a. True b.…

A:

Q: 2 2 and u4 -5 1. Let uj = u2 = U3 = 2 Let W1 = Span{u1, u2} and W2 = Span{u3, u4}. (a) Show that the…

A: Given vectors are u1→=10−52, u2→=0−125, u3→=5210 and u4→=2−50−1. Let W1=Spanu1→,u2→ and…

Q: Check whether the set S of all vectors in R¹ given by 126-85=((a+2b₁a+1,a)/a,b ≤ R} is a subspace of…

A: Given: The set S of all vectors in R3 given by S=(a+2b, a+1, a)/a,b∈R.

Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

A:

Q: 1 5 0 2 4₂ -2, 1 Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the 1 1 0…

A:

Q: Let W be a subspace spanned by the u's, an

A: Given, W be a subspace spanned by u's, and write y as the sum of a vector in W and a vector…

Q: The first four Laguerre polynomials are 1, 1- 1,2-4t +t2, and 6 18t + 9t2-1. Show that these…

A:

Q: If V is direct sum of two subspaces, then every vector in V has .representation

A:

Q: 1 1. Let ui = u2 = 2 and u = U3 -5 Let Wi = Span{u, u2} and W2 Span{u3, u4}. %3D (a) Show that the…

A:

Q: Let V₁ = 1 -1 3 4 Choose the correct answer below. 11 10 and w= 4 1 9 Is w in the subspace spanned…

A:

Q: 13. Find a basis for the subspace spanned by the vectors What is the dimension of the subspace? C100

A:

Q: Consider Sspan 1 -3 5 3 -10 10 What is the dimension of S? -3 10 -10 which is a subspace of R³ Find…

A:

Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

A:

Q: 8 UH⠀⠀ 5 10 Let v₁ = 1 -1 Choose the correct answer below. and w= 5 5 Is w in the subspace spanned…

A:

Q: 7. Let W be the subspace spanned by the u's, find the vector in the subspace W that is the closest…

A: The following is the MATHEMATICA CODE required to perform the operation specified in the given…

Q: 1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes,…

A: Given v1 = 10-2v2 = 311v3 = 612w = 321 The equation x1v1+x2v2+x3v3=w will have a solution if the…

Q: t ₁, ₂ and 3 be the columns of A, let B = {a₁, a2, ã3} and let H = span(B). a. The number of vectors…

A: Given A is a 3*3 matrix and B is set of vectors containing columns of matrix A and H= span(B).

Q: Find a projection of a vector 1 2 3 4 onto the subspace 2 5 -OD span 4 2 5 7

A:

Q: Find the closest point to y in the subspace W spanned by v₁ y = 5 1 1 15 - 1 1 - -1 2 V2 - 3 1 0 2…

A:

Q: a2 E R³ are subspaces of R³? (No justification necessary.) Which of the following sets of vectors аз…

A: Vector subspace : A subset W of a vector space V  over the scalar field K is a subspace of V if and…

Q: Is the following set of vectors in R 3 linearly dependent: {(1, 0, 3),(2, 1, -2),(0, -1, 8),(7, 2,…

A: The solution is given as

Q: P₁1 = P₂1 = P31 = P1 = P2 = What is the matrix P = (P; ;) for the projection of a vector b E R³ onto…

A:

Q: Let I2 E R 21 = 13 + #4, D2 = #3 – 14 13 14 Show that V is a subspace of R“. Find a basis for V and…

A:

Q: Let W be the subspace spanned by u, and u₂, and write y as the sum of a vector in W and a vector…

A: