(1): All vectors of the form (a,0,0) that is S={(a,0,0):u = R} Show that the following sct is subspaces of (2): All polynomials a +ux +u,x +u,x' for which u, = 0 s-{peP:p-a +ax+a,x+a,r for which a, - 0}

Q: Stretched by the vectors v1 = (1,1,1,1), v2 = (1,2,4,5) and v3 = (1, -3, -4,-2) USR Find an…

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Q: - (-, s) Find a basis for the subspace W C R', consisting of all the vectors orthogonal to the…

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Q: 3. Let V1 and V2 be subspaces of R" (over R) Their intersection V=V,nV, is the set of 2 all vectors…

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Q: Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the…

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Q: 13 - Which one of the followings is NOT the subspace of R? ? =O W = {(a,2a): a e R} W = {(a, a + 1):…

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Q: Let V be the subspace of R' spanned by the vectors below: u = (1,2, 1,3,2), Uz = (1,3, 3,5, 3), Uz =…

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Q: i) Determine the linear mapping T : R3 → R² which maps the basis vectors {(1,0,0), (0, 1,0), (0,0,…

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: Let U C R’ be the subspace generated by (1, 1, 1, 0, 1), (2, 1, 0, 0, 1), and (0, 0, 1, 0,0). Let V…

A: The given problem is related with linear algebra. Given that U ⊂ ℝ5 is a subspace generated by 1, 1,…

Q: Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: The given vectors are                                   -3110, -12613, 3-55-6, -33-23…

Q: {l: ol E M2x3: a = b = c = -3d } be a subspace of M2x3- Let W = d Then dimension of W is Оз 1 О4 O 2…

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Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: Let {v1 = (1,2,3,5,9), v2 = (3,1,2,8,9), v3 = (2, -5,5,9,4)} and {u1 = (0,1,1,1,2), u2 = (0,2, -2,…

A: The given question is related with vector space. Given that , v1 = 1,2,3,5,9 , v2 = 3,1,2,8,9 , v3 =…

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

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Q: 1 5 0 2 4₂ -2, 1 Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the 1 1 0…

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Q: 1 for which x value span the vector subspace? -1 13 - 2 -1 O A) 2 в) .1 O C) 0 D) 1 O E) -2

A: We have to find x

Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: 1. Let v, = (43 2 1), v, = (-2 0 -1 0), v3 = (0 3 0 1) a) Find the subspace of R* spanned by these…

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Q: Let V be a vector space and W₁, W2 be subspaces of V. Then verify that W₁ + W₂ = {w₁ + W₂ : W₁ € W₁…

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Q: ii) Two subspaces of R3 are U = {(x,y, z) : x – 3y – 2z = 0} and W = %3D {(r, y, z) : x – y = 0}.…

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Q: Verify all vector space axioms under the given operations (x,y,z)+(x',y'z') = (x+x'+1,y+y'+2,z+z'+3)…

A: The objective of the question is to verify if the given operations satisfy all the axioms of a…

Q: (a) Find orthonormal vectors 91, 92, 93 such that 91, 92 span the column space of 1 2 1 A - 1 -2 4…

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Q: Let U, W be subspaces of R" and assume UnW = {0„}. Prove that dim(U + W) = dim(U)+ dim(W). Here U +…

A: We have to prove given result:

Q: (a) Determine whether the set of all vectors of the form (a,b,c), where b= a+c, is a subspace of R³.…

A: Consider the subset S of ℝ3 defined as, S=(a,b,c)∈ℝ3 | b=a+c Take  a1,a2,a3,b1,b2,b3…

Q: Let I2 E R 21 = 13 + #4, D2 = #3 – 14 13 14 Show that V is a subspace of R“. Find a basis for V and…

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Q: Consider the subspace plane H spanned by two vectors U1=[-2,1,1] u2=[1,1,1] Find the orthogonal of…

A: U1=[-2,1,1] U2=[1,1,1] vector b = [2,2,2]to find the orthogonal distance…

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: Hello , I need help in Algebra a, 6, c E R. \ be Which of the following are subspaces of the R3 (a,…

A: Definition: The subset W of a vector space V is said to be a subspace if it satisfies following two…

Q: The set S = {(2a, b, a - b): a, b = R} quos & jonai (o) tails wol2 woled old is a subspace of R³.…

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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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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.