Express the following as linear combinations of u= (2, 1, 4), v= (1, -1, 3), and w= (3, 2, 5). (a) (-9, – 7, – 15) (b) (6,11,6) (c) (0,0,0) (d) (7,8,9)

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A:

Q: If u = 7i - 2j+3k and v = -i+3j + 5k then Proj,v is

A: Given, u=7i-2j+3kv=-i+3j+5k

Q: If u = 2i - 3j + k and v = i + j - k, then u x v is:   (2, 5, 3) (2, 5, -3) (2, 3, 5) (2, -3, -5)…

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Q: Find S ∩ T, (S ∩ T)c, Sc ∩ Tc, S ∪ T, (S ∪ T)c, and Sc ∪ Tc (1) S = (0, 1), T = [1/2, 3/2]

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (4, 0, −3, 5), v = (0, 2,…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Suppose that a linear transförmation / satisfies T(u,) = T(u,) = -1 -2 Find T(4u, - 3u,). T(4u, -…

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Q: 2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?

A: Given that, u→=1-12 and v→=2-11 We have to find the vector w→ for which the set u→, v→, w→ is…

Q: 1. Determine whether w=(3,1,5) is a linear combination of u=(0,-2,2) and v=(1,3,-1).

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Q: Let u= (-1, 1), v=(-3, 4), and W= (o, - 2). Find u - v + 4w

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Q: 4-Find the coordinates the front trace F for line AB, if A(2, 1, -2) and B(3, 3, -5). * O (1,-1) O…

A: A=(2,1,-2) B=(3,3,-5)

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

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Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (4, 0, −3, 5), v = (0, 2, 5, 4)

A: Given a vectors,

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: i. Find proj,u and projų v u = (2, –2), v = (3,1)

A: Given,  u=(2,-2) ,  v=(3,1)    We have to find vector projection of v on u

Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: What is the normal line to the line that passes through (-8 , 0) and (-1, 3) 3x-7y = - 24 O (x/8) +…

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Q: Express the following as linear combinations of 1= (2, 1, 4), v= (1, – 1, 3), and w= (3, 2, 5). 8.…

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Q: 6. Evaluate u x v, where u = -e, - 2e, + 2e,, v = 2e, - 2e, +e,.

A:

Q: For what values of c is the set {t +3, 2t +c2 +2} linearly independent?

A: The given set: t+3,2t+c2+2

Q: 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), = (1,2, 1), v = (-…

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Q: i. Determine whether the set is linearly dependent or linearly independent. S = {(-2,1,3), (2,9,…

A: Note :- Due to our guidelines, we can solve only one question plzzz reupload rest of question and…

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: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

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Q: Find image of a and preimage of b T(v1, v2, v3) = (4v2 – v1, 4v1 + 5v2) v = (2, -3, -1) , w =…

A: Given, T(v1, v2 , v3 ) = (4v2 – v1 , 4v1 + 5v2) v = (2, -3, -1) , w = (3, 9)

Q: 2t+9 dt (t2–14t+46) 2t + 9 2t + 9 dt (t – 7)2 – 3° J[(t – 7)2 – 3]² Option 2 Option 1 2t + 9 dt [(t…

A: Here, to rewrite the given integral: ∫2t+9(t2-14t+46)52dt...(1)

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

A: Solution is written in below steps.

Q: let u=(3,4), v=(2,-3) and w=(2,-2)  find (u*v)w

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Q: Which of the following sets is linearly independent in P2 ? {-1+ 2x,5x², –2 + 4x} the above set O…

A: A subset f1, f2, f3, ... , fn of a vector space ℙm is said to be linearly independent if…

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

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Q: 8 - If w = is a linear combination of v = and u = then r and s must be, respectively,

A: w is the linear combination of u and v then we can write  w= au + bv  Where a and b is the scalar

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: Express the following as a linear combination of u = (3, 1, 6), v = (1, -1, 8) and w = (5, 5, 7).…

A: Let's find.

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: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

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Q: Which of the following sets is linearly independent?* O M-((1,0,1),(3,0,3), (0, 0, 0) } M=((1,1,3),…

A: Since it is a multiple question. As per our company guidelines we have to solve the first question.…

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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Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (2, 6, 4).…

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Q: Let Compute θω -(2, -3) = 28 მs дw -(2, -3) = Ət w = 4xy-yz - 3xz, x = st, y = est, z = ²

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Q: If u t- dt, then o V3 2 /3 O 3 9. 3/4

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −3, −3), v = (3, −3, 3)

A: Given: u=(3, −3, −3), v=(3, −3, 3)

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: Let a = (– 1, 5, 0) and b = (3,0, – 1). Find the component of b onto a.

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Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

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Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

A: Given: u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). And, (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

Q: The set {t, –3t?} of P2 is linearly independent. O True O False

A: x=t  --------------equation 1y=-3t2  -------------equation 2now from equation 1 and 2y=-3x2means y…

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

A: The given vectors are  u=(5,1,6)v=(1,-1,5)w=(1,5,6) We have to write the given vectors in linear…

Q: Express the following as linear combinations of u = (2, 1, 4), v = (1, – 1, 3), and w= (3, 2, 5). 8.…

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Q: Find u. (v x w). (6, 6, 6) (1, 7, 0) - (0, 0, 1) > 3

A: Given that,u=6,6,6v=1,7,0w=0,0,1

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.