§3. (10 p) Let T : R3 → R3 be a linear map such that T(< 1,1,1 >) =< 2, 0, 1 >, T(< 0, −1, 2 >) =< −3, 2, 1 >, T(< 1,0,1 >) =< 1, 1,0 > . Compute T(< 1, −3,0 >).

Q: C: 1. Is there a linear map from R2 to R³ such that T(1, 3) = (0, 0, 0) and T(-2,0) = (0, 0, 0) and…

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Q: Consider a linear map T: U → R² and uí, u₂ € U. Given that T (u) = (-3,6) and T ԱՉ mapped to (0, 0)…

A: Given: Tu1→=-3,6T ; Tu2→=5,-10T.We need to find the vector which is mapped to 0,0T.

Q: Let T : R3 −→ R3 be a linear map such that T () =, T () =, T () = . Compute T ().

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Q: Consider the following linear map T: P3 → P3 defined as follows: T(ao + a1x+ azx² + a3x³) = ao +…

A: For T to be an isomorphism we must check that it is one one and onto both. And we can check it by…

Q: 1. The map T : Mat2,2(R) → Mat2,2(R) given by a +c d a b T c d а — d

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Q: 2. - For each map below, either prove that it is linear or demonstrate that it is not linear. (a) T…

A: Consider a map T:U→V is linear if    (i) T(u+v) =T(u)+T(v)   (ii) T(αu )   = αT(u)   , for all u,v…

Q: Let P denote the path that goes in straight lines from (0,0, 2) to (0,1, 2) to (1,1, 2) to (1,0, 2)…

A: Given: F→(x, y, z)=(1-z)5yxez-2z15+14

Q: .. A projective transformation M preserves the points (1,0,0), (0,1,0), and the origin of the…

A: according to question , a projective transformation M preserves the point 1,0,0 , 0,1,0 and 0,0,0…

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: ent, find a linear relation. a) vi = (2, 1, 0), V2 = (0, 1,0), V3 = (-1,2,0) %3D b) wi = (1,2, –2),…

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Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: F . dr, (c) Let f(x, y, z) = x³ + 2yª + 325 and F consists of three line segments from (1,0, 0) to…

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Q: For each of the following, determine (with argument) whether the given function T is linear. 1. The…

A: To identify which of the given function is linear transformation.