are not vector spaces? 23) Which of the following subsets of C[-1,1] 1 (x)dx 0 f(x) E CI-1,1]: a) -1 {f(x)e C-1,1]: f(-1) = f(l)} {f (x) E C[-1,1]: f(x) 0 for xe[-1/2,1 / 2]} {f(x) e Cl-1,1]: f (1) = 1} e) {f(x)e CI-1,1]: f(l) = 0} b) c) d)

Q: What is the dimension of the vector space M,x3R)?

A: SOLUTION-

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A: We have to find the scalar projection of a in the direction of b.

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

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A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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A:

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A:

Q: 2.30 Let r denote a position vector r = x= xê, (r² vector. Use index notation to show that: (a) ²…

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A:

Q: 1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*. (a) Examine if vector X = (-4,-1,6,12) is in…

A: According to our guidelines we can answer only one question and rest can be reposted.

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A:

Q: If V is a vector space then show that cV=V.

A: