Consider the basis S = {v1, V2, V3} for R, where v1=(1, 1, 1), v2 = (1, 1, 0), and v3 (1,0,0), and let T:R3-R be the linear operator for !! %3D which T(v1) = (8,- 1, 16), T(v2) = (9,0, 1), T(v3) = (- 1, 17, 1) Find a formula for T(x1, X2, X3), and use that formula to find T(8, 16, - 1). T(8, 16, - 1) = (

Q: Find the coordinates of the vector v = (7,4) with respect to the basis U₁ = (2, 1) and u₂ = (3,1).

A: The answer is given below:

Q: Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t)…

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² R², T(x, y) = (5x - 3y, 4x), B' =…

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A: We have to find all these

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Q: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

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A: The given transformation is Tx,y=x-y,y-4x and the basis B'1,-2,0,3.

Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

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A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

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Q: Find the matrix A' for T relative to the basis B'. T: R > R, Tх, у, z) %3D (у — z, х - z, х + у), В'…

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Q: The third column of the change of basis matrix from the basis B = [u= (1,1,1); v = (1,0,1); w=…

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