Calculate the given linear combination.5〈2, 2, -3〉 + 3 〈1, 7, 2〉

Q: Find u · v, u· u, ||v|2, (u · v)v, and u · (3v). u = (2, 12), v = (-3, 2) (a) u. v (b) u.u (c) ||비2…

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Q: 7. Which of the following are linear combinations of = (0, -2, 2) and v = (1, 3, –1)? (a) (2, 2, 2)…

A: A vector w is said to be a linear combination of two vectors u and v if there exist scalars c1,c2…

Q: Determine if b is a linear combination of a1, a2, and a3 a1 a2 a3 b 1 -2 -6 11 0 3 7 -5 1…

A: It is given that b is a linear combination of a1, a2, and a3.

Q: Write v as a linear combination of u,, u,, and u,, if possible. (Enter your answer in terms of u,,…

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Q: 7. Which of the following are linear combinations of = (0, -2, 2) and v = (1, 3, –1)? (a) (2, 2, 2)…

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Q: find the components of P Q. Р%3 0, 2), = (5, 0)

A: To find the components of PQ→ Given, P=(0,2) and Q=(5,0)

Q: Write each vector as a linear combination of the vectors in S (if possible).

A: Suppose that:    r= (1, 2,-2), s= (2,-1, 1) a) z=xr+ys z=x (1, 2,-2) +y (2,-1, 1) Hence,…

Q: 39. a = (-5, 12), b=(4,6) %3D %3D

A: Topic  = Vector

Q: d. Find the indicated unknown. 11. a, = -3, d = 2; a, .12. a, = 1, d = -3; a, 13. a, = 10, a, = 7; d…

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Q: S = {(2, –1, 3), (5, 0, 4)} (a) z = (5, -5, 11) %3D S, + 52 Z = 59 (b) V = | 18, 4 4 s. 22 V = (c) w…

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Q: Evaluate if a = 3, b = -2, c = 7, d = -1, and e = 0. 1. abc -42 2. cde 3. ab + cd 4. cd + ac 5. ac -…

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Q: find the components of P Q. Р%3 (1, —4), 0- (3, 5)

A: Given: P=1,-4, Q=3,5 We know that vectorAB→, where A=x1,y1, B=x2,y2 is given by AB→=x2-x1i+y2-y1j

Q: Find u · v, u· u, ||V|2, (u · v)v, and u · (3v). u = (3, -3, 5), v= (0, 6, 4) (a) u. v 2 (b) 43 u.u…

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Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (4, -3, 5), v = (0, 6, 4) (a) u: V (b) u.u (c)…

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

Q: Write v as a linear combination of u,, u2, and uz, if possible. (Enter your answer in terms of u,,…

A: the given vectors v=-1, 7, 2, u1=2,1,5, u2=3,-1,5, u3=-2,1,-3

Q: 2 Find u, 3v, v - u, and 2u + 5v. 3 u = (7, 6), v = (4, –4) %3D (a) u 3. (b) 3v (c) V - u

A: Given : u=<7,6> v=<4,-4>.

Q: 7. Which of the following are linear combinations of = (0, -2, 2) and v = (1, 3, –1)? (a) (2, 2, 2)…

A: For a,

Q: Find Jul, \vl, [2ul, , lu + v[, Ju – v\, and Jul - 2 (2, –10), v = (-4, –4) Ju| %3D |2u| %3D Ju + v|…

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Q: 2. Find u, 3v, v-u, and 2u +5v. 3. u = (5, 3), v = (3, -2) %3D

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Q: Write v as a linear combination of u and w, if possible, where u = (2, 3) and w = (3, -1). (Enter…

A: Let's find.

Q: Givenu=2+3i,v=1−2i,w=−3−6i,find|u+v|, u + 2v, u − 3v + 2w, uv, uvw, |u/v|, v/w.

A: For complex number z=x+iy |z|=x2+y2 Given complex numbers are: u=2+3i  v=1-2i  w=-3-6i Find |u+v|…

Q: Which of the following v will give a linear combination for set S = {(1, 2, -2), (2, –1, 1)}? %3D a.…

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Q: Given 4 u = 3 V = and w = -3 3 a) of u and v. Show your work. If possible, find c1, c2 such that w =…

A: Consider a set of vectors v1, v2, … , vn. Then the span of this set if the set of all linear…

Q: : A (5, -3,4), B(2,3,2) ,and C( 3,-2,-1) Known when A is translated 1(-2, 5, 3) calculates the…

A: We have to solve given problems:

Q: b = (-1, 3) and c = (–11, -2). What is c + b in component form? Enter your answer by filling in the…

A: we have to find the sum of vector.

Q: calculate the linear combinations. 5(i + 2j) − 3(2j + k) + 7(2k − i)

A: Given linear combination is: 5i+2j-32j+k+72k-i   Now, Expand 5i+2j: 5i+10j, expand 32j+k: 6j+3k and,…

Q: Given U= {1, 2, 3, 4, 5, 6, 7} A= {1, 2, 3, 4} B = {1, 2, 5, 6} C = {3, 5, 7} %3D %3D %3D %3D Find:…

A: Note- As per our policy we can answer only the first 3 sub-parts of a question. If you want…

Q: Let u = and v = . Now, w = is a linear combination of i and v. That is, w = aju + azv. Determine…

A: Answer:

Q: Given u = and v has an initial point of (3, 2) and a terminal point of (7, -1), A. Find 3v + 2u B.…

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Q: Determine if b is a linear combination of a,, a,, and aą. 1 5 3 a, = -3 , a2 = az - 6 , b= - 3 2 18…

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Q: Find u, 3v, v – u, and 2u + 5u 3. u = (4, 3), v = (3, –3) 2. (a) 3

A: Given: u=4,3   v=3,-3

Q: Which of the following v will give a linear combination for set S = {(1, 2, -2), (2,–1, 1)}? a. (1,…

A: We need to check which of the given options can be used for writing a linear combination for the set…

Q: 3. 두 벡터 u, v의 사이각을 구하여라. (1) u = (1, 2, 2) v = (3, 4, 0) (2) u = (6, 0, 2) v = (5, 3, -2) (3) u =…

A: topic - angle between vectors note : as per bartleby guidelines, we are supposed to answer only…

Q: 2. Find u, 3v, v - u, and 2u + 5v. u = (4, 3), v = (3, -7) (a) u 券 (b) 3v (c) v - u (d) 2u + 5v

A: Please find the solution below:

Q: 19, 20, 21 and 22 Find a + b, 4a + 2b, a, and a b. 21. a = 4i –3j + 2k, b=2i– 4k

A: Given that

Q: b = (-1,3) and 7 = (-11, –2). What is č + b in component form? Enter your answer by filling in the…

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Q: Find u · v, u · u, ||v||2, (u · v)v, and u · (3v). u = (3, -2, 5), v = (0, 7, 4) (a) u: v (b) u: u…

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Q: Find u - v, 2(u + 3v), and 2v - u. | u = (4, 0, -2, 5), v = (0, 6, 5, 4) %3D (a) u – v = (b) 2(u +…

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Q: Given ü = (2,-3) and = (-2,5) find ü v %3D

A: Solution is done in step 2

Q: How is w = (-3, –13, 7) e R³ a linear combination of (0, -2, 2) and (1, 3, –1)? U = | V = O A. w =…

A: Given query is to find the correct option for linear combination.

Q: b. (1, 1, 1, –1) and (1, 2, –1, 1).

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Q: write of linear Combination as a V,Vz, V3 where V= (2,7,10), V.=(1,2,3),V2=(1,3,5), V3=(1,5,9)

A: Let us assume v can be expressed as linear combination of v1, v2 and v3 v=av1+bv2+cv3…

Q: given u = and v= find 2u+5v

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Q: 19. a, =-8, a, =7; S, %3D 20. a, 3 6, а, -26; 5, %3D

A: We will find out the required values.

Q: ( 21 62) 0 7 ).v = Let u = 2 0 43 8. w = - 2 17 and s = 3 4 21 62 s can be written as a linear…

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Q: Which of the following are linear combinations of u = (0, – 2, 2) and v= (1, 3, – 1)? (a) (2,2,2)…

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Q: Find u, 3v, v-u, and 2u + 5v. u (5, 3), v (4,-5) (a) u (b) 3v (c) v-u (d) 2u + 5v

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Q: 8, 43 17 Let u = and s = = 3 4 62 s can be written as a linear combination of uv and w as follows:…

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Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (5, -2, 4), v (0, 7, 4) (a) u: V (b) (c)…

A: Dot product of two vectors u=<a,b,c>,v=<x,y,z> is defined by, u.v=ax+by+cz Norm of a…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.