Let W be the set of all vectors with x and y real. Find a basis of W1 x + y,

Q: Prove that the vectors (1. 1. 0) (1 2 3) and (2. –1 5) form a basis for R3

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Q: Let B = {1, x, x², x*} be an ordered basis for P3. Find the coordinate vector of f(x) = 4x3 – 72² +…

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Q: Let B = (1, x + 8, (x – 1)², 5x³) be an ordered basis for P3. Find the coordinate vector of %3D f(x)…

A: We have used the standard basis C {1,x,x^2,x^3} to write the coordinate vectors for f and each…

Q: Determine whether the set (a) spans R3, (b) is linearly independent, and (c) is a basis for R3.S =…

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Q: Let W be the set of all vectors with z and y real. Find a basis of W. x + y.

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Q: Let u and v be distinct vectors in a vector space V. Show that {u, v} is linearly dependent if and…

A: We have to show:Let u,v ∈ V , u ≠ v.{u,v}  is linearly dependent <=> u or v is multiple of…

Q: Find x with respect to the standard basis corresponding to the coordinate vector [x]g and basis B.…

A: here we have to find the x with respect to the standard basis corresponding to the coordinate vector…

Q: Let B be the basis of R² consisting of the vectors and let C be the basis consisting of {B} Find a…

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Q: Let B be the basis of R² consisting of the vectors and let C be the basis consisting of Find a…

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Q: Let B = (1, x, x², x*) be an ordered basis for P3. Find the coordinate vector of 8x – 6x2 – 9x + 3…

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Q: Determine whether th e set ẞ is a basis for the vector space V

A: Vector space  ,          Now  use definition of basis to check given set is basis of given…

Q: Determine whether the set B is a basis for the vector space V.

A: Given :           V = P2 , B = 1 - x, 1 - x2, x - x2   To determine the set B is a basis for the…

Q: Find the dimension of the vector space V and give a basis for V. V = {p(x) in P, : xp'(x) = p(x)}

A: We have to find the dimension of the vector space V and give a basis for V.

Q: Let {v1,…,vn}{v1,…,vn} be an orthogonal basis of RnRn. For any vectors x,yx,y in RnRn show that…

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Q: ow that the following vectors are an orthogonal basis for R, and express x as a ear combination of…

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: Let u and v be two vectors in R°. Determine the most general condition under which {u, v, u × v}…

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Q: Let W be the set of all vectors with z and y real. Find a basis of W [z +

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Q: Let S = {V1, V2, V3} be a basis for vector space V. Then show that T = {w1, W2, W3}, where w1 V1 +…

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Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = - 823 6x? –…

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Q: a Construct the arthogoral basis of set T= {v, v2, v3} for R3 Where 日。目 v, = 9 V2 = vz = Express the…

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Q: Determine whether the set B is a basis for the vector space V.

A: V=P2  ,B={ 1,1+2x+3x2)

Q: Let V be the set of all vectors of R3 of the form (0, a, a²) with the standard operations on R.…

A: (i) By the given definition, V=0, a, a2∈R3:a∈R. For 2 vectors u,v,w and x,y,z, vector addition is…

Q: Show that if S is a set of n distinct vectors that span an n dimensional vector space v, then S is a…

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Q: Let W = {ax? + (b-a)x + (a+b)| a, b e R}. Find a basis for V and find the coordinate vector for v =…

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Q: Let V be a vector space, and let v1, V2, V3, V4, V5 E V be distinct vectors in V. If B = {v1, V3,…

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Q: 4. Let {V1, ... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that Σ (х - V,)…

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Q: Let W be the set of all vectors with z and y real. Find a basis of W

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Q: Let {v1, v2, . . . , vk} be a linearly independent set of vectors in a vector space V. Delete the…

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Q: Let V be a vector space that contains a linearly independent set {u1, U2, U3, U4}. Describe how to…

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Q: Consider the subset V of the vector space R4. (a) explain why V is NOT a basis for R4 without…

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Q: Given the vectors V1 = (x, 1,1), V2 = (1, x, 1) and V3 = (1,1, x). S = { V1, V2, V3} of the set Find…

A: 3 vectors form a basis of R3, if they are linearly Independent. Vectors are linearly Independent if…

Q: Let {u1, ·.., Un} be a list of vectors in an n-dimensional vector space V and let B be a basis for…

A: Given V is a n- dimensional vector space. Let B be a basis for V. Let B=v1, v2, …, vn. Let u1, u2,…

Q: Determine whether these vectors are a basis for R' by checking whether the vectors span R', and…

A: Introduction: For a vector space V, a set of vectors B is referred to as a basis for V if B spans V…

Q: Let {u1, u2 U3, U4, U5} be an orthogonal basis for R5, y a vector in R5, W1 = Span{u1, uz} and W2 =…

A: For orthonormal basis of R5, {u1, u2, u3, u4, u5}  We know that span of the elements is orthogonal.…

Q: Find a such that the set W = {1+ 2x - x², ao + x + x²,5 - 5x+7x²} is linearly dependent in the…

A: To find the value of a0 such that the given set is linear dependent in the vector space Rx≤2.…

Q: Let W be the set of all vectors with x and y real. Find a basis of W+. [x+y]

A: To find a basis of WT

Q: Let W be the plane 3x + 2y − z = 0 in R3. Find a basis for W⊥.

A: Let W be the plane 3x + 2y − z = 0 in ℝ3. Find a basis for W⊥. We know that dimension of W and…

Q: For the set of vectors S = {(1,2, –2), (0, 4, 2), (2, 1, – 1)}, show that S forms a basis in the…

A: Given: Set of vectors S = {(1,2,-2), (0,4,2), (2,1,-1)} To prove: S is a basis for R3 Concept Used:…

Q: Let V = C? be the vector space over C and let a = {u = (i, 1), u2 = (1,0)} be vectors in V. Show…

A: Vector space and basis

Q: .Let W = {ax? + (b-a)x + (a+b)| a, be R}. Find a basis for V and find the coordinate vector for v =…

A: find basis of V then will find coordinate

Q: 2. Consider the set (a) Verify that this is an orthogonal basis of R³. (b) Write the vector v = as a…

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Q: Let u, v, and w be distinct vectors of a vector space V. Show that if {u, v, w} is a basis for V,…

A: Let u,v,w ∈ V  a vector space over a field F such that u≠v≠w . Let {u,v,w} be a basis for V. Because…

Q: Let x, y, and z be vectors in a vector space V. Prove that if x + y = x + z then y = z.

A: if, x+y=x+z we use transportation and solve it

Q: Write x as the sum of two vectors, one in Span {u,,u,,u3) and one in Span (uA. Assume that (u,,.u}…

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Q: Show that the given vectors form an ortho­gonal basis for R2 or R3• Give the coordinate vector [w]of…

A: Orthogonal basis:        Let v1,v2,.....,vn be linearly independent vectors in Rn, if v1,v2,.....,vn…

Q: Let B = {v1, .. be a linearly independent set in Rn. Explain why B must be a basis for TR"

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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.