3) Let V = R[t]≤2, W = M2×2(R) with standard basis B = (1,t, t²),C = (M₁, M2, M3, M4). Suppose : V → W is some linear map such that, under the complexified basis Bc, Cc we have (a) (b) (c) [vc] = 1 2 0 1 -1 22 2 1 4 0 What is yc(1 t²) What is (1 +t) (not the complexified function, the original) What is [y]

Q: 2. Let v, = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, V2, V3} %3D is a basis for…

A: 1. A finite set of vectors v1,v2,...,vn of a vector space V over a field F is said to be linearly…

Q: Suppose , t2, ., , are linearly independent. Prove that S is linearly independent where (a) S=…

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Q: Let v = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, v2, V3} is a basis for R³.…

A: We know that,                           Tx1,x2,x3 = x1T1,0,0+x2T0,1,0 +x3T0,0,1

Q: Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the…

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Q: Let V=R². For (u₁, U₂), (v₁, v₂) € V and a € R define vector addition by (u₁, ₂) (V₁, V₂) = (U₁ +…

A: The given vector space is .For any  and , the vector addition and scalar multiplications are defined…

Q: 14. Let P₂ be the vector space of polynomials of degree ≤ 2. Let D = {1 + t, 1 − 5t, 2 + t²}. Check…

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Q: 4. Consider V₁ = 5 2 V₂ = 6 a 3 V3 = (a) Show that V₁, V2, V3 are linearly independent. (b) Find the…

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Q: 2. Let B₁ be the basis 2²e², re², e² of V = span(2²e², zeª, z), and B₂ be the basis of that the map…

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Q: . Show that (x, y) = 4x1y1 – 7x2y2 for vectors x = (x1, x2) and y = (y1 y2) in R2 defines an inner…

A: Given two vectors x and y in R2. We need to show that the given function in x and y defines an inner…

Q: V is the linear span of the polynomials a =x' + 2x – 2x + 1, ß=x' + 3x² - x+4, y = 2x +x - 7x – 7…

A:

Q: 3. Let V be the vector space of polynomials with coefficients from R. a) Show that the following…

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Q: Consider the ordered basis B = {(1,-1,0), (1, 1, 1), (0, 1, 1)} of R³. the coordinate vector v =…

A: Consider the ordered basis B=1,-1,0, 1,1,1, 0,1,1 of ℝ3.   To Give: The coordinate vector v=-2,-1,0…

Q: 8. Let V={(x,y)x,y € R}. Define addition on V as follows: (x»x)+(x,y)=(x +2x, 1,y+Y,+2) Find the…

A: To find zero vector of V

Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

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Q: 2. Find vectors v, w E R³ such that v + w = (1,3,7), v is parallel to (1, 0, 1), and w is orthogonal…

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Q: (c) Let V and W be given as above. By using linear extension method, determine whether V is…

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Q: II) Consider the standard basis e, e2, e3, e, of R. Suppose the linear map T : R- R satisfies 0.…

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Q: V is a finite dimensional vector space s = {a1,a2, ., an} C V and Sp(S) = Vaccepted 3i fori S is…

A: Note: In the question, ∃ should have been ∀. Otherwise, the statement won't be valid. We are given…

Q: 5. Determine whether or not the following vectors i R³ are linearly dependent: (1, –2, 1), (2, 1,…

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Q: (a) Let B= {b1, b2}, where bị =(:) and by = G) Is B an orthogonal basis for R2 ? O True O False (b)…

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Q: 2. Let ū = (-1, 2, 1), ở = (1, – 1,–1) and w = (2, 3, 0). Find the coordinates of (2,4,4) with…

A: Using gauss Jordan elimination method to find the value.

Q: (a) Find the vector Q=[0, a,0] such that the resultant of the vectors: P=[5, 7, 8], Q=[0, a, 0] , R=…

A: Hey, thanx for your question. According to our policy I m answering question first. Please post the…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = (V1 + V2, V1 - V½), v =…

A: To solve this problem we follow the following steps : Finding image :  Write down the given…

Q: Let ū = -4î + 4ĵ – 3k and i = î – 25 + 2k. (a) Let w = proj, ū. Compute w. (b) Compute u-w and show…

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Q: Consider the basis 5 = {v1, V2, V3} for R°, where v: = (1, 1, 1), v2 = (1, 1, 0), and va = (1,0,0),…

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Q: What is the dimension of P₂, the vector space of all polynomials of degree at most two? b. Find the…

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Q: Parts of this question are independent (a) Suppose īj, ūz ā, b,č 4, det[ū, ī2 č =-1. Find det [v, ūz…

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Q: 3c

A: Step 1:a) To evaluate the adjoint (or conjugate transpose) of the linear operator T on the inner…

Q: Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2x?, –1 +x+x², 1…

A: Consider the provided question, Given that,  B=1+x-2x2, -1+x+x2, 1-x+x2B'=1-3x+x2, 1-3x-2x2,…

Q: or function By – k1 z) + ay (kz y + z) onal, then the values

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Q: 14. Given that the linear map F: C→Cover C be defined by F(x, y, z) = (2r-y-z, 4x-y) relative to the…

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