Suppose ū = (3, 2, 4), v = (-3, –3, 1) and w = (2, –4, 1). Then: i - w= v . w= ủ · (v+ w)=

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (3, 11), v = (-4, 3) (a) u: V (b) u. u (c)…

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Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: Calculate v x w: v = (5,6,2), V X W W = (5, 4, 7)

A: Step 1: Step 2: Step 3: Step 4:

Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: (c) Determine whether the set R², with the operations (x₁, y₁) + (x₂, y/₂) = (x,,0) and c(x, y) =…

A: Let V be the vector space if  1 If u,v∈V  then u+v ∈V 2.  u+v=v+u 3. (u+v)+w=u+(v+w) 4. Identity…

Q: Which 2 points are on the line (x,y) = (3,7) + k(-1,2), k E R Select one: (-1, 2), (3, 7) (3,7), (2,…

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Q: Let f {(0,-3),(9,4),(-6,9)} and h={(-6,4),(-3,9)}. Find fo h. foh= (Use a comma to separate ordered…

A: The given functions  and .The objective is to find the composition function .

Q: Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, -1, -2). Find z, where 2u + v – w + 3z = 0. z =

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Q: Can we write v = (1,5,4) as a linear combination of u = (1,3, -2), uz = (2,7,-1), ug = (1,6,7) ?

A: If there exist a,b,c∈ℝ such that au1+bu2+cu3=v then we can say  v as a linear combination of u1,u2…

Q: 30. (-2, 2) reflected through the origin is a. (2, 2) b. (2, -2) с. (-2, 2) d. (-2, -2)

A: Rule:- A point  (x,y) after reflection through origin becomes ( -x , -y )

Q: Suppose that u · (v × w) = 3. Find (a) u · (w × v) (b) (v × w) · u (c) w · (u × v) (d) v · (u × w)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Let u = (2, -1,3), v = (3,0,1) and w = (-1,-1,3). find all values of I, m and n such that lu + mv +…

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Q: Find u · v, u · u, ||v||². (u - v)v, and u · (3v). u = (3, 12), v = (-2, 3) (a) u. v (b) u.u (c)…

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Q: Find u (v x W). u = (3,3,3) (5,9, 0) V = w = (0, 0, 3)

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Q: Find u v. = (9, 2) v 3 (-8, 4) V: U V D

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Q: V=(2,7,10),V%=(1,2,3), Vz (1,3,5),Vz=(1,5,9)

A: Let V=aV1+bV2 +cV3 where a, b and c are constants.

Q: Find u (vx w). =(5, 5, 5) v = (1, 9, 0) w = (0, 0, 4) U =

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Q: Express the following as a linear combination of u (2, 1, 5), v (1,-1, 4) and w = (6, 8, 6). (9, 14,…

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Q: (e) Determine whether the set S = {x² - 2x₁ x³ +8₁x¹-x²₁x²-4} spans P₁.

A: To find- Determine whether the set S = x2 - 2x, x3 + 8, x3 - x2, x2 - 4 spans P3.        Concept…

Q: Find u•v, V•V, ||u||^2, (u•v)v, and u. (5v). u=(2,0,-3,4), v=(0,5,4,5)

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Q: Find w such that 2u + v u 3w = 0. (0, 2, 7, 5), v = (-8, 4, -3, 1) 1 -- (-) W = 3 -

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