Let V = R?. For (u1, U2), (V1, V2) e V and a e R define vector addition by (u1, U2) H (v1, V2) := (u1 + vị + 1, u2 + v2 + 3) and scalar multiplication by a O (u1, u2) := (au, + a – 1, auz + 3a – 3). It can be shown that (V, H, O) is a vector space over the scalar field R. Find the following: the sum: (9, –1) H(-5, 7) =( the scalar multiple: 10 (9, –1) =( the zero vector: Oy =( the additive inverse of (x, y): B(x, y) =(

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: Let V = R². For (u₁, U2), (v1, v2₂) € V and a € R define vector addition by (U1, U2) = (v1, v2) :=…

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Q: Do only question 6

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A: GIVEN THREE VECTORS v1, v2, v3 belongs to R^3 are linearly dependent

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A: Cross product

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Q: Compute (u v Ղա • Ա. . — u = (i, 7,6), v = (2, -7i, 1+i), w = (7-i, 7i, 3 + 6i) u · v) ա • Ա —

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Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

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Q: Do question 10 only

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Q: Do only question 4

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Q: Do question 9 only

A: Step 1: Compute the Gradient of 𝑓Given f(x,y)=x2ey,Compute the partial…

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Q: If d is a scalar multiple of b, then ax%. Select one: True False

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