Which of the following sets are subspaces of R³? OA. ((-4x, 9x, -2x) | x arbitrary number} OB. {(x, y, z) | -9x+2y+ 8z = 4} OC. {(x, y, z) | x, y, z>0} D. {(x, y, z) | x+y+z=0} OE. {(x, x-6, x - 5) | x arbitrary number} OF. {(x, y, z) | 6x + 5y = 0, -3x - 4z = 0}

Q: Which of the following is the dimension of the subspace b W = :a = b - c and a, b, c,d eRC R* ? (a)…

A:

Q: Given the inner product space (R³(R),+,.,-), where oy = 3x₁₁ + 2(x₂₁ + X₁3₂) + 3x₂y₂ + 2X3Y3, X =…

A: This is a problem related to inner product space. Please see the next step for details.

Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

A:

Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

A:

Q: (1) Consider the space M2×2 (R) of 2 x 2 matrices equipped with the usual addition and scalar…

A:

Q: Consider the line V = {(t,t + 1) |t € R} in R. Let V be the real vector space with vector addition e…

A:

Q: Consider the line V = {(t,t + 1)|t e R} in R. Let V be the real vector space with vector addition e…

A:

Q: F(x, y, z) = (z sint z sin(ar), e²y-2 X b+y

A:

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

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: Q6: Show that R³ = {(x1,x2, x3)|lx1,x2, x3 E R} is a vector space

A: Vector space is the field created by set of vectors with specified direction and magnitude, usually…

Q: 42. Rather than use the standard definitions of addition and scalar multiplication in R®, let these…

A: The given question can be solved as shown in step2.

Q: Q3 shew that W2 = subspace of R2 is a

A: To show any subset of vector space is a subspace , prove the following condition : Set is closed…

Q: Find the dimension of the subspace U={[a+c, b+c, a+2c+b] | a, b, c in R} Select one: a. 2 b. 4 c. 1…

A: We have given a subspace ,  U = a + c , b + c , a + 2c + b / a , b , c ∈ ℝ We need to find dimension…

Q: Can someone help me answer this question with all the steps thank you.

A:

Q: Q2. Let V = {(a, b, c, d) : b + 2c + d = 0} and W = {(a,b, c, d) : a + 2b = 0, c = 5d} be two…

A:

Q: Q4) Determine whether the set S is linearly independent or linearly dependent a) S = {(2,1,–2),…

A:

Q: 3. Determine whether the set W = {(0,x2, 3, x4) : where x2 and x4 are real numbers} is a subspace of…

A: Subspace of a vector space

Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

A:

Q: , Y, 2, W) w) 3. Using methods of linear algebra verify whether Question a. span{(2,0,0), (1, 3,0)}C…

A:

Q: The set of all vectors in R squared  that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy  3x+4y=1  is not a subspace of R squared.  i.e.…

Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

A:

Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: Let W be the subspace of Rª defines as X1 X2 W = {x = ER : : x1 – 3x2 + 4x3 – x4}. %3D x3 X4…

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: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: Let W (w1, w2, w3) = UxV (cross product) such that U(-3, 3, -3) and V(1, 1, 7) %3D find w2 Answer:

A:

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

A:

Q: Choose all that apply for the set S2 e R : 3x1 - x2+ 5x3 12 x3 O S2contains the zero vector. O Szis…

A: The given set is                                S2=x1x2x3∈ℝ3 : 3x1-x2+5x3=12

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: a+b |a, b, c e R) of My? a +e 6- a каn C? b-c ,каn C What is the dimension of the subspace U kan Ç О…

A: