linear algebra) 1. if the p=(u,v,w) where u,v,w are vectors. Show that a. |p|<=|u|+|v|+|w| b. |u|<=|p|, |v|<=|p|, |w|<=|p|

Q: 81. Given r = (-3, 4) and s = a. Find the product ||r|||s||. (9. – 12). b. Find r· s. c. Based on…

A: Given:r=-3,4 and s=9,-12Formula:u=u.u

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=&lt;-6, 3, -2&gt;

Q: What geometric relationship must two vectors have in order for ||u + v|| = ||u|| + ||v|| ?

A: The expression ∥u+v∥denotes the norm of u+v, ∥u∥denotes the norm of u and ∥v∥denotes the norm of v.…

Q: Suppose that i and v are vectors in R". If ū · ū = 4 and ||v|| = 9, then || 18

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Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: Find u, u = (-1, 4), v = (4, 5) (a) ||u|| v, uv, and d(u, v). (b) ||v|| (c) (d) U V d(u, v)

A: The given vectors u=-1, 4, v=4, 5. We have to find the values of u, v, u.v, du, v.

Q: Suppose that u and v are two vectors with |u| = 1, |v| = 4 and u · v = −2. a. Compute |u + v|. b.…

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Q: Let u and v be vectors in R". Show that ||u – v||? – 2||u – 2v||2 + ||u – 3v||2 = 2||v||? %3D

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Q: 39. The vertices A, B, C of a triangle have position vectors a, b, c respectively. The area of this…

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Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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Q: Find each vector sum u + v. a. u = (1, 4), v = (2, −2) b. u = (3, −2), v = (−3, 2) c. u = (2, 1), v…

A: a). b).

Q: Match each property with its name. Inequality of arithmetic and geometric means Commutativity of dot…

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Q: Let v = (a) 27 t (5, 2, 5) and w= (1, 5, 0). - = 4w = (b) Let 3 (t, 1, 0). For which value(s) of t…

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Q: Let -3 ----------- V3 2 V1 = 6 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are in…

A: Let and

Q: Suppose that u, v, and w are vectors such that = 3, = -2, = 5, llull Evaluate the following…

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Q: 2. Let a, b and c be vectors in R". Prove that (a) a and (a c)b - (a - b)c are perpendicular; a b…

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Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

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: Solve for all vectors X so that × X = .

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Q: Suppose u, v are vectors in V. Then ||u – 2v|| = Select one: O a. ||u|| + ||v||' +2Re O b. ||u|| +…

A: Consider u and v are two vectors in V. The objective of the problem is to find the value of…

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: For any vectors i, vin R', we have |a+ = |u + |). True O False Reset Selection

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Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: Let A and B be vectors in R" and let c be a real number. Then (1) ||A|| 2 0, and || A|| = 0 if and…

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