Consider the basis S = {V₁, V₂} for R2, where v₁ = (1, 1) and v₂ = (1, 0), and let T:R² → R² be the linear operator for which T(v₁)= (1, 3) and T(v₂) = (-6, 1) Find a formula for T(x₁, x2), and use that formula to find T(7,-4). T(7,-4)= ( i i

Q: Specifically a DiffEq problem. Question in pic below. I'm not quite sure why my answer is wrong.

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Q: Consider the basis S = {v, v2} for R2, where v = (1, 1) and v2 = (1, 0), and let T:R? – R2 be the…

A: Step:-1 Given transformation is  T :  ℝ2 →ℝ2 Tv1 =1, -6  and   Tv2 =-12, 1 Here, v1=1, 1,  v2=1, 0…

Q: Consider vị =[1 v2 = | 1) and v3 = ( 0 ) as vectors in R³. Let T: R3→R³ be a linear operator such…

A: We have to find out solutions

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

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Q: Consider the basis S = [v;. V2. V3} for Rº, where v = (1, 1, 1), v2 = (1, 1, 0), and v3 = (1,0,0),…

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Q: . Consider V1 1 and v3 = V2 = .0. 0 ) as vectors in R3. Let T: R3→R3 be a linear operator such that…

A: The solution is given as

Q: [C] Is the system of vectors X1 = (2, 2, 1)", dependent? Ху — (1,3, 1)7, X3 = (1, 2, 2)" linearly

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Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

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Q: Let c1 (t) = ei + 7 sin(t)j + t*k and c2 (t) = e-Sti + 5 cos(t)j – 7t*k. (Enter your solution as a…

A: Given: Let c1(t)=e5ti+7sintj+t4k and c2(t)=e-5ti+5cos(t)j-7t4k. To Find:      ddt[c1(t)+c2(t)]

Q: 1. Show that the given vector functions are linearly independent on (-∞, ∞). X₁ (t) = = 0 X₂ (t) H…

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Q: Let C₁ (t) esti + 7 sin(t)j + tªk and c₂ (t) = e¯5ti + 3 cos(t)j - 4t¹k. (Enter your solution as a…

A: Given that c1(t) = e5ti + 7sin(t)j + t4kc2(t) = e-5ti + 3cos(t)j -4 t4k

Q: Consider the basis S = {v,, v2, V3} for R, where v = (1, 1, 1), v2 = (1, 1, 0), and v3 = (1, 0, 0),…

A: Given that S is basis contains 3 elements S = {v1, v2, v3}, where the basis element is given as:…

Q: Let V = P² be the vector space of polynomials of degree at most 2, and let B be the basis {f1, f2,…

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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: Consider the basis S - (V₁, V₂} for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the…

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Q: Find the standard T₁: R² T₂: R² A = A' matrices A and A' for T = T₂° T₁ and T' = T₁ ° T₂. R², T₁(x,…

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Q: show that the given vector functions are linearly independent on (−∞,∞).

A: To show that the given vector functions are linearly independent x1t=   et-et,        x2t=etet

Q: Consider the basis S- (V₁, V2, V3) for R³, where v₁ -(1, 1, 1), v₂-(1, 1, 0), and v3 - (1,0,0), and…

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Q: Let D = (d₁d2₂ d3) and F = {f₁.f2.13) be bases for a vector space V, and suppose f₁ =3d₁-d₂ +5d3, f₂…

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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: For convenience, we write the coefficients uj,¿ in the vector {u} = (u₁, U₂,. where l - 1 + i + (N +…

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Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

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Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Find the coordinate vector of w relative to the basis S = { u1, u2} for R u 1 = (4, – 4), u 2 = (4,…

A: Given: u1=4,-4u2=4,4w=0,24

Q: Consider the basis S= {V1, V2, V3} for R, where vV1 (1, 1, 1), v2=(1,1,0), and v3 =(1,0,0), and let…

A: Given:       Tv1=8,-1,16        Tv2=9,0,1         Tv3=-1,17,1      v1=1,1,1       v2=1,1,0…

Q: The vector x = H vector [2]8 = [2] A 1 B2 C3 in R² relative to the orthogonal basis B = What is the…

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Q: R³ given by 3x₁ + 4x2x3 7x1 ·x2 + x3 5x1 + 6x2 - X3 and then calculate T(-7, 1, 9) by directly…

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Q: Find the standard matrices A and A' for  T = T2 ∘ T1 and T' = T1 ∘ T2. T1: R2 → R2, T1(x, y) = (x −…

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