Question 9 Solve the problem. Let H = a + 3b + 4d c+d -3a-9b+ 4c - Sd -c-d Find the dimension of the subspace H. dim H=3 Odim H-1 dim H = 2 : a, b, c, d in R ancama dim H = 4

Q: 1. If A = find A1000 by diagonalizing. )Show every single step for your work).

A:

Q: The subset in the form where x and y are real numbers, is a subspace of R2 if Select one: O x + 0…

A:

Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

A:

Q: Use least squares to find the orthogonal projection of u onto the subspace of R* spanned by the…

A:

Q: Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each subspace (and…

A: First we have to construct a 2x3 matrix of rank 1. then find the vector in the subspace (row space…

Q: Given = 2 2 -6 3 6 1-0 and -6 36 find the closest point to in the subspace W spanned by

A: Given,        To  find the closest point to v in the subspace W spanned by

Q: State the dimension of the following subspace, The solution space {(a,b,c): a-3b+c=0, b-2c=0,…

A: We have to find the dimension of the subspace.

Q: = Complete the following truth table. Use T for true and F for false. You may add more columns, but…

A:

Q: Determine; if W = the set of all odd functions is a subspace.

A:

Q: Given = 5 # -6 find the closest point to in the subspace W spanned by 3 2 6 and 0 -6 -7 -54

A:

Q: The integers 1 through 36 (inclusive) are used once each as the coefficients for six vectors in P 5…

A: We know that, A subspace is a vector space that is contained within another vector space. So every…

Q: Only use the definition of subspaces, determine whether U = {(-a,–2B+a,a – 3,)| a ER and ß E R} is a…

A:

Q: Given 7 = find the closest point to in the subspace W spanned by -2 and -3 -1 30

A:

Q: 1 :) Given v = -2 -5 -0 and 2 -16 6 -9 4 -4 0 -6 4 find the closest point to v in the subspace W…

A:

Q: 1. (a) Find an example of a set of vectors in R³ that is linearly independent but does not span R°.…

A:

Q: a 12 Let A 0 a 1 For what value of a is A diagonalizable? Explain your 00 a answer.

A:

Q: Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1} a subspace of R*? Show the details of %3D your…

A:

Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

Q: The closest point is

A:

Q: 5.6. Are the polynomials 1-2x+3x², 2+x-x², 1-2x+x² linearly independent in the vector space P₂? If…

A:

Q: 5. Let H = {(a - 3b, b-a, a, b): a, b E R}. Show that H is a subspace of R¹.

A:

Q: Use the Row Reduction Algorithm to solve the following. Describe the solution set of Ax=b in the…

A: Given system of linear equations:Ax=bWhere A=[3−377164−491022−11−2−3−5]  ,  b=[−24−355]The augmented…

Q: Let A be a 80 x 90 matrix (80 rows and 90 columns). Does the homogeneous 0 always has nonzero…

A:

Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

A:

Q: Let V be the subspace of R spanned by v = . Describe V+ by finding a basis of

A:

Q: lem #1: Let v₁ = (2, 1, 0, -1). v₂ = (0, 1, 2, 1). and b = (1, 7, -1, −5). Let W be the subspace or…

A:

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: Find a set of vectors that spans the subspace W CV of solutions to the following linear systems. 1.…

A:

Q: T: ([₂]) = 3x1 +4x2 x1 - 2x2 4x1

A:

Q: For which value of a is the solution set of the following system х+5у +z —D b — 5 2х — 4y — z —а+b-3…

A:

Q: Find the bases of the subspaces and determine their dimensions.

A:

Q: Let A be the matrix consisting of columns equal to the given vectors. A = [w, | w] -1 5 -4 -2 Then…

A:

Q: Find a basis for the subspace of Rª spanned by the following vectors. Answer: 5 -14

A:

Q: . Let W₁ -00--00 and W₂ = (b) 1 equal to (a) 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3

A: We have to solve given problems:

Q: Show that the set of all polynomials of degree at most 3 forms a subspace of Pn.

A: