One of the following is a subspace of R³. Which one? The set of points (x, y, z) in R3 such that (a) x + 2y3z = 4. I - - 1 -= (b) 2 3 (c) x+y+z = 0 and xy +z = 1. (d) x = −z and r = z. (e) x² + y² y-3 I (f) 2 5 Answer: ( y+2 Z == . 4 = <= 2. ) is a subspace of R³.

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

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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…

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Q: One of the following subsets of R² is not subspace. Select one: а. X1 S={ X1=2x2} b. S={ ,X1 =X2} C.…

A: We will check that which subset is not a subspace of R2

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: 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: 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: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x² + x² +…

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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…

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Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

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Q: Determine whether S={a, +a,x+a,x :a, +a, +a, = 0} is a subspace of P.

A: Here S is a subspace of P2

Q: Let V₁ 1 -2 3 2 {V1, V2,V3}. V₂ = 2 -2 V3 7 8 7 - 10 and u = Is u in the subspace of R4 generated by…

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Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

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Q: Determine whether each of the following sets are subspaces of R³ with the standard operations. sure…

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Q: What is the area of ​​a square whose side measures (x2-2x+1)?

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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…

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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: Determine the dimension of the subspace of R consisting of all XeR* such that x1 + 2x, = 0 and X3 –…

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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: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 19, Un 28 国 26 20 -2 -26…

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Q: Q6: Explain whether the following sets are not subspaces of R" for the appropriate value of n. a a a…

A: We have to show that given set are vector subspace or not

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

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Q: 2. Find the projection from R³ onto its subspace spanned by (1, 2, −1)ª and (1,1,2).

A: Given that We  have  to  find  the projection from   onto  its  subspace spanned  by  .Let   be…

Q: 2. The subspace in R3 is a plane whose equation is x+y+z=0 x-2=0 x-2y+z=0 (a) (b) 2-0 (c) y-2--0…

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Q: The four subspaces are Nullspace, Column space, Row space, and Null space

A: Please give a helpful review after seeing the quality of solution provided. Each and every step is…

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: Given that = 2 = -------- y = V3 = 3 10 and h -12]

A: As per the guideline, I am supposed to solve only first question from the given problems.

Q: Given that V1 = 5 3 V2 = 2 } V3 = 3 7 " 11 10 For what value(s) of h will y be in the subspace of H…

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

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Q: 1. The linear span of a set S is the (a) largest subspace contained in S. (c) smallest subspace…

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Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

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

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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: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

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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

Q: [{-----} x+y+z=-7 A. B. Which of the following sets are subspaces of R³ ? C. D. Z X Z +2=0} 7x -5x…

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Q: Find the adjoint of the matrix, then use the adjoint to find the inverse if possible. [-1 3 2] A= 0…

A: (i) The given matrix is: A=-1320-2110-2 Adjoint matrix is the transpose of the cofactor matrix. Find…