Let B = {v1, v2, v3} be a basis for R3. For any u, v E R³ define (u, v) = [u]%[v]B• (a) Is (,) an inner product?

Q: Let T : R2[x] → R2[x] be given by T(a+bx+cx2 ) = a + b(x+ 1) + b(x + 1)2 . Let v = x + 1. Find a…

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Q: Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find <u, v>

Q: Let V=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ +…

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Q: Let V = R². For (u₁, U2), (v₁, v₂) € V and a ER define vector addition by (u₁, U₂) (V1₁, V₂) = = (U₁…

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Q: Let f E P(R) be a polynomial of degree n. Let yo,..., Yn be the dual basis of 1, x, x²,..., x". Show…

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Q: Does V {x2 + x, 1 + x + 2x³, x3 2x, x + 3x²} span P3? Is it linearl- - independent? Is it a basis of…

A: That's easy. Have a good day!!!

Q: 3. Let T : R² → R² be defined by T = X Y -x+y x-y

A: 3. Given that  be defined by:

Q: Let V be the vector space of functions spanned by Nπ B = {b₁ = 5 sin x + 7 cos x, b₂ = 3 sin x + 9…

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Q: Let T be a linear operator on R³ such that the rational form of T is [T] B = 0-20 1 0 for some…

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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: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find the .

Q: 201 Give monsingural uragonal matrix. Call a diagonal matrix ever be 21) Show that ( (2) where x, y,…

A: A 2×2 matrix is diagonalisable if A has two different eigenvalues.

Q: Consider P2(R) with its basis B = (x, x + 1, x² –- 1). Find [x2 + 3x + 5]B.

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Q: Let V = R?. For (u1, u2), (v1, v2) e V and a e R define vector addition by (u1, u2) # (v1, v2) :=…

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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: Consider the vector space V over the real numbers, consisting of all polynomials of degree less than…

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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,…