2. Let x = (1, 1, 1, 1)" and y = (8, 2, 2, 0)". (a) Determine the angle 0 between x and y. (b) Find the vector projection p of x onto y. (c) Verify that x – pis orthogonal to p. (d) Compute ||x – p||2, ||p||2, ||x||2 and verify that the Pythagorean law is satisfied.

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A: Linear transformation: Let us consider a mapping T:V→W defined as T(v)=w where v∈V and w∈W [  v is…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = (V1 + V2, V1 - V½), v =…

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Q: (b) (5 marks) Let u = 3i - 5j, v = -2i + 7j, Show that (u +v) (u - v) =||u||^2- ||v||^2

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Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: Use the function to find the image of v and the preimage of w. T(V1, v2) = (Vị + v2, V1 - V2), v =…

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