a) [The set v = U2 U1- - V2. [2].110 b) a basis for R². The set S = If v E span{v₁, U₂}, then U = ◆ 3 4 [8].0₁ = [2]. U1 c) The set S = span R2. {0.4} {[5].[B]-[]} +

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Q: be the map O Let f Sending cach Complex number

A: The detailed solution is as follows below :

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A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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Q: Let v1 =[1,4,-2] , v2 =[-2,-3,7] , b =[4,1,h] FIND all value(s) h such that b is in span{v1 , v2 }

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Q: . Let V be a vector space, and {v1, ··· , vn} be a set of vectors that spans V . Show that the set…

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Q: Determine whether the set of polynomials 10. i (I+ x2, x + X2, 2 t x} is a basis forr Pe (TR).

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Q: Use the function to find the image of v and the preimage of w. T(V₁, V₂) =(√² V₁. √2, - V2, V1 + V₂,…

A:

Q: | Let v₁ = (1, −1, 1, − 2), v₂ − (−1, 2, −1, 1), v, −(−2, 1, −1, 5). Determine whether {V₁, V₂, V3}…

A:

Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) 1, (u, w) = :8, (v,…

A:

Q: 2) Let R real numbers, define = x,Y1 +4x2y2 + 6x3Y3 for x = (x1,x2, X3) and y (y1,y2, Ya). Is inner…

A: Let V be a vector space over ℝ.An inner product <·,·> is a function V×V→ℝ with the following…

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Q: find the value of a for which       [ 4 ] v = [ a ]       [-4]       [ 3 ] is in the set…

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Q: 3. [6 points] Consider the vector space V = P, over the field of real numbers F = R. Is the vector 4…

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Q: Show that the set of complex number C={x+iy|x and y are real, i2=-1} is a vector space. Verify each…

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Q: Let f be the function from {a, b, c, d} to {1, 2, 3, 4} with f(a) = 4, f(b) = 2, f(c) = 1, and f(d)…

A: For bijection, the function needs to be one to one and onto.

Q: The vectors ~={]-=[B]-=[C]~-[&] -=[] V3 and v5 -2 8 V₁ 2 1 V₂ V4 -17 generate R³. Find a subset of…

A:

Q: 2. Let V be the set of all ordered pairs of real numbers, and consider the following addition and…

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Q: Show that the complex numbers 2 + 3i and 1 – 2i generate the vector space

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A: The norm of x is the distance between a point x to the origin.

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

Q: 6. Can any of the given sets of 3-vectors below span the 3-space? Why or why not? (a) [1 2 1] [231]…

A: We have to check whether the given set of 3-vectors span the 3 space. (a) 1 2 1, 2 3 1, 3 4 2 (b) 8…

Q: La) Emplain why is entive ? the function fcz) = 5z"-6+zcosz -ze

A: z=x+iy⇒5z4=5x+iy4=5(x4-6x2y2+y4)+5i(4x3y-4xy3) --->eqn(1)⇒xcosz=x cos(x+iy)=x(cosxcos hy-i sin x…

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Q: Let X₁ = [1 3 −1 1]²‚×₂ = [3 −1 3 1]′, and x3 = [-1 2 −3 1]. Is b = T an element of span{X₁, X₂,…

A: No, we can write it.

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A: We have to determine the dimension of the subspace M of M2(R) .