Write v as a linear combination of u1, u2, and u3, if possible. v = (1, 2, 3, 5), u1 = (1, 2, 3, 4), u2 = (−1, −2, −3, 4), u3 = (0, 0, 1, 1)

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

A: Given:  v = (-1,7,2) u1 = (1,3,5) and u2 = (2,-1,3)  and u3 = (-1,3,1) we need to find v as a linear…

Q: Find u x v, v x u, and v x v. u = (5, 6, -4) v = (-6, -9, –8) (a) ux v (b) v xu (c) v x v

A: We can make it easier for you

Q: Find u · v, u· u, ||v||, (u· v)v, and u (3v). u = (2, 11), v = (-5, 2) %3D

A: Given u=2, 11, v=-5, 2

Q: d) Determine if b is a linear combination of a1, a2 and a3? 5 -6,b -2,a2= [2] ,A3=

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Q: Let b1 and b2 8 Either show that is a linear combination of b1 and b2, or show that it is not a…

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Q: Find u x v, v x u, and v x v. u = (2, -9, –1) v = (9, -2, -6) (a) ux v (b) v xu (c) v x v V

A: We need to find cross product.

Q: If w = is a linear combination of v = and u = then r and s must be, -1 respectively, (а) 3, 1 (b)…

A: Option C is correct option.

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 and w, if possible, where u = (2, 3) and w = (3, -1). (Enter…

A: Let's find.

Q: Find u-v, 2(u+3v), and (2v-u). u=(7,0,-6,9), v=(0,2,9,7)

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Q: Find u x v, v x u, and v x v. 3D(-7, 1, 2) 3(4,7, -6) u = (a) u x v (b) (c) V X V

A: Solve

Q: Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1,…

A: This question is related to linearity of vectors, we will solve it using given information.

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (1, −2, −3), v = (3, 1, 0)

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Q: Find u x v, v x u, and v x v. u = (3, -8, -3) (6, -6, -7) V = (a) u x v (b) v x u (c) v x v

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

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

A: The given vectors,  u=5,-2,4, v=0,7,5

Q: Suppose v4 = 20 – 02 + 503. Let w = 601 + 202 – 303 – 204. (a) Write w as a linear combination of…

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Q: Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1,…

A: We have to write the linear combination of the given data.

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: value of x , y , and z.

A: We will find x y z

Q: Find u x v, v x u, and v x v. u = (3, -3, -1) v = (-2, –7, -5) (a) ux v

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Q: is a linear combination of vi = V2 = V3 = u ulgn ihi

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Q: Find u x v, v x u, and v x v.

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

A: Answer:

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

A: Given vectors, u = (2,-3) and v = (4,3) To find: u.v, v.v, ||u||2, (u.v)v, u.(5v) calculations are…

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 - v, 2(u + 3v), and 2v - u. u = (6, -2, 4, 3), (-2, -1) (a) u - v = (b) 2(u + 3v) = (c) 2v -…

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Q: let R = (-2, 7). Calculate the following: The components of u = PŔ, where P = (1, 2)

A: Given,               R=(-2, 7)   and   P= (1, 2).    The components  of u=PR⇀=?

Q: Determine if b is a linear combination of ā1, ãz and dz. 6 = 2 3 16

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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 x v, v x u, and v x v. u = (5, 6, -4) v= (-6, -9, -8) (a) ux v (b) v xu (c) v x v

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Q: Choose which variables are basic and which are nonbasic: X1 X2 X3 S1 S2 S3 P 0 8 1 -4 0 40 4 160 1 8…

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Q: If possible, write -3 -z- 2r² as a linear combination of 2 +z + x², 2+ 2x + z and 3+ 3x + 2x2.…

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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. = (3, 4, 4, 0, 4), v = (-3, 3, 6, 8, -5) %3D (a) u - v = (b) 2(u…

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Q: 国~ Let aj = a2 -24 and b: For what value(s) of h is b a linear combination of aj and a2?

A: Explained below

Q: Find A -B x C, (Ax В): (В х) if A%3 2а, — х, а, — 2а, В %3D 4а, + x,а, + 2а, and с 3 -âx + ây – x3â,…

A: see the attached image below

Q: When b is expressed as a linear combination C1u + c2v + C3W, what is C3?

A: Follow the procedure given below.

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v

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

A: Given vectors are u = 3, -3,  v = 2, 4

Q: is a linear combination of Vị = V2 V3 = u= ulgn ihs O

A: We have to check for linear combination

Q: Express the GCD of (210,162) as a linear combination of 210 and 162.

A: Here, we have to find the GCD of (210, 162) as a linear combination of 210 and 162. For this, we…

Q: Find u v, u u, v, (u v)v, and u (3v). u -(5, -2, 4). v-(0, 6, 4) (a) (b) () (d) (u-v)v (e) u (3v)

A: Solution: The objective is to find the required values

Q: Which of the following sets are linearly dependent? Select all possible answers. 3 9. 4 12 } -3 "000…

A: We will find out the required solution.

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: Əw Use the appropriate Chain Rule to calculate ди Write your answer in terms of u and v. 4ху, х %3D…

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Q: Find u v, u· u, ||v||2, (u · v)v, and u · (3v). = (2, 11), v = (-5, 2) %D (a) A. n (b) u u (c)…

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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.