In Exercises 1-10, determine whether the indicated subset is a subspace of the given Euclidean space R". 1. {[r, -r] | rЄ R} in R² 3. {[n, m] | n and m are integers in R² 5. {[x, y, z] | x,y,z ER and z = 3x + 2} in R³ 7. {[x, y, z] | x,y,z Є R and z = 1, y = 2x} in R³ 9. {[2x₁, 3x2, 4x3, 5x4] | x; Є R} in R³

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Q: 28. Find the unit vector in the opposite direction to 7 –j + k.

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Q: 3- A discrete topological space (X,T) is: a-To-space, b-T₁-space, c- T₂-space, d- No one.

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Q: 2] -1 1] a. Find SVD from A 1. A = [4 | b. Find SVD from A invers 2. A = [; : : 8] 1 0 0 0 a. Find…

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Q: 2) One of the following subsets of IR2 is not subspace: a) S = {, xeR} b) s = {], = x3} %3D %3D e) s…

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Q: Let U, A, B, and C be defined as shown below. U= [ a, b, c, d, e, f, g, h, i, j } A = { d, e, g, h,…

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Q: In Exercises 1-10, determine wheth indicated subset is a subspace of the Euclidean space R". 1. {[r,…

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Q: 3. Two vector norms 11·11 and III'lll on a if there exists Space X are equivalent C70 such that…

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Q: Show that ([0,1] spack по matric matriz, is complete uniform norm

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Q: 32. Show that, in a normed space, x x implies -(x1 ++Xn) → x.

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Q: 18. Find the vector u in 2-space of length 2 that makes an angle 0 4.

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Q: OR SECTION 13.6 1. Let S be a nonempty, closed, convex set in R" that does not contain the origin.…

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Q: 9) Suppose u, v € V, where V is an inner product space, and ||u|| = ||v|| = 1 and (u, v) = 1. Find u…

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Q: 4. Find a translation that maps A(2, –3) onto B(4,–2).

A: Given that: A(2, -3) and B(4, -2)