If U = {(x, y, z) : 3x -y-2z = 0} is a subspace of R, then U = %3D %3D %3D A) {(r, y, z) : r - y+ = 0} B) {(3t, -t, 2t): te R} C) {(3t, –t, –2t) : te R} D) {(r, y, z) : -3r + y +2z = 0}

Q: Find the equation of a plane containing point R(1,0,1) and parallel to the plane 2x-y+z=1. a…

A: The general equation of the required plane.

Q: Which one of the following is a subspace of the vector space M2 (R) of 2 x 2 matrices? ss (X) the…

A: .

Q: Use Axioms only to prove that the the solution to the equation 2x + y + 3z = 0 is a subspace of R³.

A: The given equation .To prove that the solution to the equation is a subspace of .

Q: Let x, y, z be (non-zero) vectors and suppose w = -12x - 6y + 2z. If z = 4x + 2y, then w = x+ A.…

A: given that  w= -12x- 6y+2z  and if z=4x+2y then  w= -12x-6y +2(4x+2y)  = -12x -6y +8x+4y w= -4 x -2…

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: The vector x is in a subspace H with a basis ß = {b1,b2}. Find the ß-coordinate vector of x. b₁ =…

A:

Q: Q: Let W, ={(a, B.Y, 8): a=y+28, y= 28} and W2 {(a, B.Y, 8):a-y-0} be two subspaces of V,(R). Find a…

A:

Q: I) Show that W = {(a, b,a-b): a, b e R) is a subspace of R³ and find its dimension.

A: W = {(a, b, a - b) : a, b ∈ R} Clearly, W is a subset of R3.     Let, (a1, b1, a1 - b1), (a2, b2, a2…

Q: Prove that the set of vectors of the form (a, b, c) where b = a +c is a subspace of R³.

A: According to the given information, it is required to prove that:

Q: Which one of the followings is NOT the subspace of R2 ? W = {(0,–2a): a e R} - W = {(2a, a): a e R}…

A: To find which one is not a subspace.

Q: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

A:

Q: (14) Find the dimension of the subspace H = a + 4b+c+2d a + 2b + d a +5b+c+3d b+d = ahader } : a, b,…

A:

Q: 5. Let W be the subspace of the vector space V = R spanned by the vectors =(1,3, 1, -2), B = (-3,…

A:

Q: a + 3b + 4d C+ d 14) Let H = :a, b, c, d in R -3a - 9b + 4c - 8d -C - d Find the dimension of the…

A: image is attached with detailed explnation

Q: Find the next vector spacing and wrap A = 1(x + y?) +jv² + zx) + k(z? + xy)

A:

Q: Let u = (18,1,0). Find the orthogonal projection of u onto the subspace W spanned by the…

A:

Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: Let W be the subspace spanned by the u's. Write y as the sum of a vector in W and a vector…

A:

Q: Let U and V be the subset of R' defined as U = { (a,b.c,d) : 3b-2d-a = 0 } and / = { (a,b,c,d) : a=c…

A:

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Q-2: a) combination of the vectors X = (1,2,3,0) and Y = (2,1,6,0). b) a linearly independent set of…

A:

Q: A line l passes through the point P(2,4, 3) and is parallel to the vector (3, 2, –3). | At what…

A: Proceed as shown below

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

A:

Q: A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

A: the scalar equation of a plane with normal  vector n=(A,B,C) is  AX+BY+CZ+D=0

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: function V(x,y,z) = x² + xy + yz and a vector A = x² + xy + yzź are given. a) Find VV(x, y, z). b)…

A: Given function v(x,y,z) is

Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

A:

Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

A:

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: Show {s,t,4s-3t)|s and t are in ℝ} is a subspace of ℝ3

A: Let A= {s,t,4s-3t)|s and t are in ℝ}To show A is vector space it is enough to show that   v1,v2…

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