Task 1 Verify that a given mapping L is linear if: L(x,y,z) =(3*, y, 2z),x,y,z E R. If L is a mapping then determine a) Im L b) Ker L

Q: 5. Write a rule for the translation of a point of the plane figure above. A. (x,y)→ (x-2,y+3) B.…

A: Translation of a point of the plane means moving all the points of that plane to a new coordinate.

Q: -2 4 and w= Let u = -3 -2 For what values of h is wm the plame Spanned by ut and v ? 3=

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Q: Verify that {u₁,4₂} is an orthogonal set, and then find the orthogonal projection of y onto…

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Q: b) Is there a linear map T: V → W, where dim V = 3, dim W = 4, rank T = 2, and dim ker T = 1?

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Q: Verify that {₁,₂} is an orthogonal set, and then find the orthogonal projection of y onto Span…

A: To Find:a) Verify that  is an orthogonal set.b) The orthogonal projection y onto span .

Q: Verify that {u₁,u₂} is an orthogonal set, and then find the orthogonal projection of y onto…

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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: (3 marks) Let r Є R and u = v ■- (2) - (+) w- () (+), -4 " W = For which values r = R is the set {u,…

A: The vectors are linearly independent for all r except 1. Explanation:

Q: , Y, 2, W) w) 3. Using methods of linear algebra verify whether Question a. span{(2,0,0), (1, 3,0)}C…

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Q: Describe each line. a) [x, y] = [2, -5] + t[0, 1] b) [x, y] = [3, 7] + [2, 0] c) [x, y, z] = [-1, 3,…

A: Solution below

Q: W and V are linear spaces with dimension 2, the base of each of which is (e,, ez). If the linear…

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Q: 7 and bɔ 3 4 Let S be the parallelogram determined by the vectors b, and let A= Compute the area of…

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Q: Evaluate ef zy³dx. ry³dx + x³dy, where C' is the rectangle with vertices (0,0), (4,0), (4,5), and…

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