Let v = −→P Q, where P = (−2, 5), Q = (1, −2). Which of the following vectors with the given tails and heads are equivalent to v? (−3, 3), (0, 4)

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: 1. Determine R21, the vector from P2(5, 2,–4) to P¿(3,–1,0). А. 4ах + ay · 6az В. 2а, + Зау — 4а, С.…

A: P25, 2, -4 & P13, -1, 0

Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

A: Linearly independent

Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Find the cross products u x v and v xu for the vectors u = (4,4,0) and v = (0,2, - 5).

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Q: Without doing any calculations, explain why the following sets of vectors are linearly dependent:…

A: Since you have posted multiple question with multi part we are supposed to give solution of first…

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: Find the initial point A of the vector that is equivalent to (3,7), and whose terminal point is…

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Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩.Express y as the sum of two vectors: one parallel to x, the other…

A: Given that: x=(1,1,1) and y=(0,3, -2) are two  vectors. Let us say,  w = (a, b, c ) is a vector…

Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: Find the angle between the pair of vectors below. u = (2,3) and v = (-2,5)

A: Given query is to find the angle bothe vectors.

Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

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Q: For what value of x, are the vectors vị 3 V2 = 3 and v3 = 2 linearly dependent? 3 Select one: 10 9.…

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Q: Find the values of x such that the angle between the vectors u = (2, 1, -1) and v = (1, x, 0) is…

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Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

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Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

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Q: Determine R21, the vector from P2(5, 2,–4) to P1 (3, –1,0). 2аx + Зау — 4а, — 2ах — Зау + 4a, | 4ах…

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: Which of the following pairs of vectors are linearly independent? Ou= (1,0) and w = (0,2). Ou =…

A:

Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

A: It is assumed that the question asks to find the value of k for which the vectors will be parallel…

Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors <-14x, 2,1> , <2, 3x2, 10> To find:- positive value of x when both…

Q: given the vectors from R. 203, v2 (1 3 0), v3=( 2 4 -1) 203 belongs to span{v,, V2, v3}. Select one:…

A: We have to check the span

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Q2: Determined the component of the vectors at each point…

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Q: For each pair of vectors, calculate projvu and the vector component of u orthogonal to v. (a) u =…

A: Vector components

Q: For the vectors u = (- 3,5) and v = (- 5,2), calculate proj,u and scal,u.

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Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

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Q: For which value of k the two vectors u=(3,3,k) and v= (-4,8,1) are orthogonal? *

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Q: Find the vector v with the given length and the same direction as u.||v|| = 5, u = (√5, 5, 0)

A: Let the vector u is:   Now, The modulus of vector u is :                                     The…

Q: Determine R21, the vector from P2(5,2,–4) to P1 (3,–1,0). 2аx + Зау — 4а, —2ах — Зау + 4az 4ax + ay…

A: Consider the following vectors: P→1=3ax-ayP→2=5ax+2ay-4az…

Q: 2. For what values of h the vectors , ü2 = 9 ,ūz linearly independent? are

A: To find : For what value of h  given vectors are linearly independent    We have given the…

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

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Q: Give a set of vectors that is linearly dependent for P3 Show your work.

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Q: Determine if the vectors of R³; vị = (1, –3,0), v2 = (3,0,4) and vz = (11,–6,12) are linearly…

A: Given vectors are: v=(1,-3,0) v=(3,0,4) v=(11,-6,12) Form a matrix by having rows as given vectors.…

Q: the vector from P1(1, 3) to P2(4, –2) is

A: Given :

Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: Use the points P(3, 1) and Q(7, 1) to find position vectors equal to PQ and QP.

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.