Consider the follouing subset of R4 W = #1 + *3 = 19 +I4 Is W a subspace of R? If it is, describe it geometrically as a point, line, plane, a 3-space, or all of Rª.

Q: Suppose U, W,, W, are subspaces of a vector space V. Show that (Un W,) + (UnW,)Cun (W, + W,) Find…

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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: Consider the vector space P, of polynomials with real coefficients of degree at most two together…

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Q: 2. Let а — lb +c а S = {[a – b ,b,c € R a a. Show that S is a subspace of M2x2. 31 -2 31 5 b. Is |…

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Q: Suppose that U and V are both subspaces of R . Prove that their intersection U ∩ V = {v : v ∈ U…

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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: Please go through each option with explanation

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Q: Consider set V = { (x, y ), x,yER} with the following operations: addition (x1, y1) + (x2 , Y2) = (2…

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Q: 2. Determine whether W = {a + br + cr?; a, b, c € R, a · b.c= 0} is a subspace of P2.

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Q: Let W be the set of all vectors of the form a b where a - C = 4 and b - C = - 5. Lc Then, W is a…

A: Given: W=abc|ac=4, bc=-5 To prove W is subspace or not.

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: The shape's vector set is a subspace of R3

A: solution :-

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: 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: 2. Let W1 and W2 be two subspaces of V, such that dimg(W1) = dimg(W2) = 2. Suppose that the only…

A: here we can use linear combination to prove that given set is linearly independent.

Q: Let U1, U2 and W be the subspaces of a vector space V. Prove or give a counter example if V = U1 ⊕ W…

A: U1,U2 and W be the subspaces of a vector space V.

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

A: The solution is given as

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: Describe all linear maps ƒ : R² → R² that are projections with image the subspace ((1,2)).

A: f: ℝ2→ℝ2Subspace =1, 2

Q: Determine whether the subset W below is a subspace of R³ with the standard operations Justify your…

A: To check if the subset W is a subspace of R3 with the standard operation. W={(s, t, s + t)| s and t…

Q: Explain why the subset а — b S = a +b а,bER -26 – 3a of R3 is or is not a subspace of R³.

A: Given subset of R3 is  S={a-ba+b-2b-3a|a,b∈R} explain if S is subspace of R3

Q: Show that if Z subspace of a space Y and Y is a subspace of a space X then Z is a subspace of a…

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Q: C: Let A = (v₁,...,04) be any list of 4 vectors in the vector space V. Let B = (v₁-V2, V₁-V3, V1-V4,…

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Q: Let A = {(1, –2,0), (0,0, 1), (-1, 2,0)}. Determine if A spans R. If A does not span R°, give a…

A: To find wheather A spans R3 we have to check if it forms a basis in R3

Q: a b a b M22 space of a, b, c e R and K= 20 - Which of the sets is a subspace under standard…

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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: The set of all points in R3 satisfying x + y - z = 0 is a subspace. Note that the set of point…

A: It is known that any subspace of ℝ3 should contain an additivities identity element 0, 0, 0.

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…

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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.