Let T : R² → R² by T(x) = A˜, where 1. Find ker T 2. Find a basis for im T. A-[¹₁2] Α = -3 -6

Q: Find the coordinate vector of x = basis B [X] B = = M 4 LOJ of R³. 0 {Q.48} [B] with respect to the

A: The coordinate vector of x with respect to basis B={v1,v2,⋯,vn} is [x]B=[a1a2⋮an] such that…

Q: 3. The set B = {1-t², t-t²,2-2t + t²} is a basis for P2. Find the coordinate vector of p(t) =…

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Q: { be a basis for R? . Find the vector æ if [æ]R =| 3 Let B 8 x = x = 6. x = x = H 00

A: Given that B=11,21 be the basis for R2. We have to find vector x if xB=23. Since, xB=23 Hence,…

Q: 1. Let u = [1 0 1]",0₁ = [1 1+ T -i]¹, 1+i 1- - V₂ = [2i 1 0], and v3 V3 = [2 −1 1]². Let = V1, V2,…

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Q: 5. Let T: R3 →R³ be a linear operator and B = {V1, V2, V3} a basis for R3. Suppose -1] T(v1) = 2…

A: It is given that T:ℝ3→ℝ3 be the linear operator and B=v1,v2,v3 a basis of ℝ3. Tv1=-121,…

Q: 7. What basis for V = M(n, R) does Theorem 3.3 i) yield when applied to T(A) = A + AT, with W M(n,…

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Q: 7. Let T:R2-R2 be the reflection about the line 3x=2y. 1 0 [T]B = ( (a) Find a basis ß={v1,v2} for…

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Q: 10. Let P denote the vector space of polynomials of degree at most k. Let T: P3 → P2 be the function…

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Q: 32. Let p, (t) = 1 +t², p2(t) = t – 3t², p3(t) = 1 +t – 3t2. || - - a. Use coordinate vectors to…

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Q: To get a feel for higher order ODES, show that the given functions are solutions and form a basis on…

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Q: Find the coordinate vector [x]R of x relative to the given basis B= {b1. b}. 2 1 b2 = - 4 %3D [X]g…

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Q: Using n=4 equal-width subintervals, approximate the area of the region bounded by the graph of, ƒ(x)…

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Q: 6. Find the following. a. Find the B-coordinate vector of s(t) = 4+5 sin?(t) given B = {1, sin(t),…

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Q: find the matna X for T elative to the basis B: T:R'R*, TG j) = (x-J,y-ta), 8'-{(1, -), CO 3)} I D

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Q: .3 Let W = span{x, x' x³, x>} in C[0,1]. Use Gram Schmidt to find an orthogonal basis for W.

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Q: 4. Given the vector equations below, find the value of the scalar k, such that a = kb. [T4] * = + *…

A: To find the value of a scalar k by the given vector x→=35y→+25z→

Q: Find the dimension and a basis of U = r2s+t 0 -3r s-t r, s, tER

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Q: I would appreciate step by step explanations so that I may understand the solution! Thank you very…

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Q: Problem 2 : Let T: R3[r] → R3[r] be the linear operator defined as T(p(x)) = (x+ 6)p' (x) + p"(x),…

A: Solution

Q: Let A = [A]s 1] -2 3 = 12/2 (a) Let S = of A with respect to the ordered basis S. (61.61.61.69) 00…

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Q: The set S = { 1, sin(x), cos(x) } is : Select one: O a. orthonormal O b. Dependent O c. Basis for R3…

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