Let V = R. For u, v E V and a E R define vector addition by uvu+v - 2 and scalar multiplication by a Du := au -2a + 2. It can be shown that (V,B, ) is a vect over the scalar field R. Find the following: the sum: 0-6= the scalar multiple: 00 the zero vector: Ov= the additive inverse of a Br=

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A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

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A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

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Q: Which of these is a valid expression in index notation which outputs a vector? A d,F B © c) E F. F…

A: Given: Objective: Identify the valid expression in index notation that outputs a vector.

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Q: Find the scalar triple product u (vxw). u. (vxw) = u = (-6,1,3), v = (3,6, - 8), w = (-4,3,2)

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Q: Thanks it makes sense. One follow up question, is it enough to show that addition is not…

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Q: Find u · (v x w). This quantity is called the triple scalar product of u, v, and w. u = (4, 4, 4), v…

A: = i(5·0 - 0·(-1)) - j (1·0 - 0·0) + k (1·(-1) - 5·0) = i (0 - 0) - j (0 - 0) + k (-1…

Q: Find u ∙ (v × w). This quantity is called the triple scalar product of u, v, and w.u = (2, 0, 1), v…

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Q: Which of these operators produces a scalar when it acts on a vector? A B D Ⓡ u. V V D2 V. Vx

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Q: 9. Let V be the set of all ordered pairs of real numbers, and consider the following addition and…

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Q: А = 1 1 1 3 4 -3 - 1 0 2 B || 8 -2 1 -3 1 0 - 4 1 1

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Q: Let u = [1, -6, 3] and v= [-3, 3, 0]T. Find the vector w = 3u - 2v and its additive inverse. W= W=…

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