5. Let T: R3 →R³ be a linear operator and B = {V1, V2, V3} a basis for R3. Suppose -1] T(v1) = 2 ,T(v2) 5,T(v3) -21 a. Determine whether w =| 1 is in range of T. 2 b. Find a basis for R(T). c. Find dim(N(T))

Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

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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: 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: 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 7 670 |--[31] - -3 -6, b 2 3 Select true or false for each statement. Let A and c = 0 []·.· 1. The…

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Q: Find the coordinate vector [x] of x relative to the given basis B = ={D₁, D₂, D3}. 1 b₁ = -1 b₂ = 4…

A: we will find the required.

Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: Her we solve the linear equation to get the solution.

Q: Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered…

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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 A 2 -5 6 ✓ 5 -2 6 Select true or false for each statement. b 2 [1].. True 1. The vector c is in…

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

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Q: 2. (а) ở and w are vectors in R? such that f(0) = w. Express f(27 – 3w) as a linear combination of i…

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Q: 36. Let T be a linear transformation from R² to R². Let ₁, 2, and be three vectors in R2, as shown…

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Q: 3) Let T d b }]= la + 1b + 1c + 5d + 2e +2f la + 2b + 0c + 5d + 3e + 1f 3a + 4b +3c + 17d+ 8e +6f…

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Q: 10. Prove that R= [(a,b) E Rx Rla s bl is reflexive and transitive but not symmetric. Reflexive…

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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: 1 17. В %3D is an ordered basis of R². = , 2 find x. 3 (a) If the B-coordinate vector of a vector x…

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Q: 5. Consider V=R². Find the coordinates of = (10, 20) with respect to the ordered basis ß= [(1, 1),…

A: we will find the coordinate vector with respect to the given basis.

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

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