Determine if the function defines an inner product on R², where u = (u, v) = ₁V₁ satisfies (u, v) = (v, u) does not satisfy (u, v) = (v, u) satisfies (u, v + w) = (u, v) + (u, w) does not satisfy (u, v + w) = (u, v) + (u, w) satisfies c(u, v) = (cu, v) > U does not satisfy c(u, v) = (cu, v) satisfies (v, v) ≥ 0, and (v, v) = 0 if and only if v = 0 does not satisfy (v, v) ≥ 0, and (v, v) = 0 if and only if v = 0 X (U₁U₂) and v = (V₁, V₂). (Select all that apply.)

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x°, -1+a…

A: given B=1+x-2x2 , -1+x+x2 , 1-x+x2B'=1-3x+x2, 1-3x-2x2 , 1-2x+3x2 b) find the coordination matrices…

Q: What is the scalar projection of vector a given by (a₁,a2,a3) in the direction of vector b given by…

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

Q: Consider the inner product space (P2, (, )) with (p, q) = p(to)q(to) + p(t1)q(t1) + p(t2)q(t,),…

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

A: An inner product on real spaces V is a function that associates a number u, v with each pairs of…

Q: Find u. v, uu, ||u||², (u - v)v, and u . u = , V = (a) (b) u. V u . u (c) || u ||2 (e) (d) (u. v)v…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Let (V, (, )) be an inner product space and let f, g be vectors in V. if || f|| = 4, ||| 5 and || f…

A:

Q: Find the Jacobian a(x, y, z) a(u, v, w) for the indicated change of variables. If x = f(u, v, w), y…

A: x=ρ sinφ cosθy=ρ sinφ sinθz=ρ cosφ

Q: If V is vector space, with u = (u, , U2) and v = (v, , v2) with u +v = (u,+v, , u2+v2) and ku =…

A: u=(u1,u2) , ku=(3u1,0) k=2, u=(-1,2)

Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

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Q: 2. fu = and v = v1, v2, V3 > are two vectors in 3-space show k that u x v= u1 U2 U3 V1 V2 V3

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Q: Consider the points + (xo, yo) (x1, y₁) (x2, 12) (X3, 13) (X4, Y4) = = (-3,-4), (-1, 1), (0, 1), X =…

A: x -3 -1 0 2 3 y -4 1 1 5 9

Q: D = 3 u=(9,-4); || u || = -√97 u=(9,-4): || u ||= √97 u=(9,4): ||u||= -√97 u= (9,4); ||u||= √97

A: given u has initial point P at (0,0) and terminal point Q at (9,-4)

Q: (H) {| R uzayı 2)

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Q: Let (V, (, )) be an inner product space and let v, w be vectors in V. If (v, w) = 7 and w = 5, then…

A:

Q: Show that the function (V1, V₂) = 2w1W2 + x1x2 - Y1Y2 +2122 defined for any vectors V₁ = (x1, y1,…

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Q: Let U = ((1, 1, 0, 1), (0, 1, 2, 3), (2, 3, 2,−1)) and W = ((1, 3, 4, 4), (1, 1, 0, 2)) be sub-…

A: The given U=1, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, -1 and  W=1, 3, 4, 4, 1, 1, 0, 2 be a subspaces of ℝ4.…

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: ^2

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Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

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Q: Determine whether u, v and w lie in the same plane when positioned so that their initial points…

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Q: Verify all vector space axioms under the given operations (x,y,z)+(x',y'z') = (x+x'+1,y+y'+2,z+z'+3)…

A: The objective of the question is to verify if the given operations satisfy all the axioms of a…

Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (7, , v.) +…

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: Show that there do not exist scalars c₁, c₂, and C3 such that c₁(1,0, 1,0) + c2 (1, 0, 2, 1) +…

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Q: Let (u, v) be the inner product on R² generated by A = 1=[ A and let u = (3,-4), v = (-4,5). Find…

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Q: Let u=<-1,1> v=<-3,4> and w=<0,-2> Find u-v+4w

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Q: 7) Find all vectors v in F such that 2v + ) -)

A: