Let V = M2x2. W. (R) = € V : a, b, cER W2(R) € V : a € R then prove that W, and W2 are subspaces of V. and find the dimension of W,, W2, and W,NW2 respectively.

Q: rove that W2 = {(a,b) E R² : a = 26²} is not a subspace of R?.

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Q: If V3(R) is a vector space and W₁ = {(a,0, c): a, c = R} and W₂ = {(0,b,c): b, c = R} are two…

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

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

Q: Verify whether the subsets of W of V = P₂ is a subspace: W = a₂x² + a₁x + ao where a₂ #0

A: The given subset W=a2x2+a1x+a0 where a2≠0 of V=P2. We have to check whether the subset is a supspace…

Q: 3. Let W = {(x,y,z): x? + y? = z}. Is W a subspace of V = R3? %3D

A: We need to check if W is a subspace or not.

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

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Q: 12): x € R. Is W a subspace of V? Expalin your 3x- Q1. Let V = R³ and W = answer? Q2. Show that M2x2…

A: The properties of subspaces: Closed under multiplication; Closed under addition; Contains the…

Q: 11. Let W be the set of all vectors of the form 5 b + b 2 с where b and care arbitrary. Find vectors…

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Q: 8. Let V be a vector space over F and v₁, ₂, € V. Then (₁₁) = (a₁v₁ + + a₂v, la,,a,F) is a subspace…

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Q: . Let u₁ = (1, -2, -1), U₂ = (2, 2,-2), and v = = (0, 0, 1). v is not in the subspace W spanned by…

A: In this question, a vector that is orthogonal to a given vector is to be determined. A non-zero…

Q: Determine whether W is a subspace of V

A: Given

Q: V₁ 1₁3 G a. Is w in (₁,₂,3)? How many vectors are in (V₁, V₂, Va)? b. How many vectors are in…

A: Three vectors v1,v2,v3 are given. (a) First one needs to check whether another vector w is in the…

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: Determine If The Subset W Is A Vector Subspace Of V = R3 w = {(x, y, z): x * y-z = 0

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Q: If V3(R) is a vector space and W₁ = {(a,0, c): a, c = R} and W₂ = {(0, b, c): b, c = R} are two…

A: Provided that V3 is three dimensional vector space over field R and V has two W1 and W2 subspace…

Q: Determine whether W is a subspace of V

A: Determine whether W is a subspace of V

Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

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Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

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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: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.

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Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

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Q: Determine whether the following sets are subspaces of R³. Realize number 4 as the span of a…

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Q: Suppose U and W are subspaces of a vector space V. Prove that if U C W, then U + W = W.

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Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y = 5 - 1 1 18 V₁ 1 - 2 - 1 3 V2…

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Q: Show that W = {a + bx² € P₂|a, b = R} is a subspace of P2.

A: The solution is given as

Q: 2. Let V = E3 and W = {x|x = a(1,0,2) + b(1,-1,3)} and S = {x\x = (x1,x2, 1)} where a and b are any…

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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: 3. This problem is about set addition and subspaces. Let d = and dz = and V = span{d}, %3D U =…

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Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.