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: Let I and g be unit vectors. Hence T-T= -G = 1. Calculate the inner products I (-1) and (T+g) -…

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Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

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Q: Let B = {(1, 1), (2, 3)} and B′ = {(5, 2), (1, 3)} be two bases for R2. [T]B= 2 3 4 7 (a) Find (T…

A: please see the next step for solution

Q: 3 Find the coordinate vector of a with respect to the basis B for R3. 2 1.

A: We find the coordinate vector.

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 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: 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: 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: 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 two bases B = {b₁,b2} and C = {₁, 2} for R² where 3 5 = = - [B]-4-[13] 4-[8]), 4-[8] =…

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Q: Find the coordinate vector (x]g of x relative to the given basis B= (b1, b2, b3}. 5 b1 , b = 5 b3 =…

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Q: Show that r|(1) and r2(1) define the same line, where rị(t) = (3, –1, 4) + t (8, 12, –6) r2(1) =…

A: Two lines have the same direction if their direction vectors v1→ and v2→ are directly proportional.…

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

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