a) tor which values on a are the vectors 87 2 -- a linearln independent?

Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

A:

Q: Find the length of the vector.v = (4, 3)

A:

Q: List five vectors in Span {V1,V2} do not sketch 4

A: Given two vectors v1=93-8, v2=-640.

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

A:

Q: Determine which sets of vectors are orthogonal.

A: Consider the given vector as -312, 241 and 1-12

Q: Suppose u = (2, 3) and ī = (3, 11) are two vectors that form the sides of a parallelogram. Then the…

A:

Q: 2. Determine whether a translation maps quadrilateral LMNP onto quadrilateral L'MNP. If so, find the…

A: We have to find the translation which maps quadrilateral LMNP onto quadrilateral L'M'N'P'.  The…

Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

Q: 4. If d and bare unit vectors and |a + 61= v3, determine (2d – 38)- (+2). %3D

A:

Q: find the diJ tance betueen the vectors

A:

Q: make an example and prove it about five vectors spanning R⁴

A: Given: Five vector spanning R4  We need to form an example and prove the given statement 'Five…

Q: A parallelipiped is constructed using vectors (8.1,2.3,0), (9.5,2.0,0) and (7.3,-2.1,7.7), what is…

A: To find the volume of parallelepiped.

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: Suppose e vectors. that a and b ave nonzero Under what ciraumstarces is comp= compas Under ahat…

A: According to the problem, we have

Q: Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly…

A: Solve the given problem.

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

A:

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: 6 2 Show that it is vectors are lineas dependent line or independent.

A:

Q: 5. Calculate the area of the parallelogram formed by the vectors (4, 10, 9) and (3, 1, -2).

A:

Q: List five vectors in Span /v,, v,}. Do not make a sketch. 1. V2}

A:

Q: Give an example of vectors in R^3 that spans R^3. (show works)

A:

Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

A:

Q: The angle between the two vectors 1= (-9, –4, 7) and v = (36, 16, -28) is Select one: True False

A:

Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: Show that if u and v are any vectors in R2, then| |u+v| |2 ≤ (| |u| |+| |v| |)2 and hence | |u+v| |≤…

A: Let the component of u and v are ; u=(u1, u2)T v=(v1, v2)T Then; This gives us the inequality;…

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

A:

Q: Find the area of triangle with the vectors p(0,1,4),0(-5,9,2) and R(7,2,8)

A:

Q: [13].The couple vectors M1 and M2 represent M2 couples which are contained in the planes ABC and…

A: Given:

Q: A set of 3 vectors in IR^4 spans IR^4. Is this true or false?

A: Given statement is, “A set of three vectors in R4 spans R4.”

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

A:

Q: Let A, B, C be points in 3-space. Suppose that AB represents u, BC represents v, AC represents W.…

A:

Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

Q: Find the length of the vector.v = (2, 0, −5, 5)

A:

Q: a. From the set of vectors{ (1, 2, –1). (-4, –5, –6), (4, 3, 10). (5, –3,2)}. select two pairs of…

A:

Q: Find the length of the vector. v - (9, 12)

A:

Q: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

A:

Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Prove that llu + vll2 + llu - vll2 = 2llull2 + 2llvll2 for all vectors u and v in Rn

A:

Q: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to…

A:

Q: For the vectors u = (-4,1) and v = (-2,3), calculate projyu and scal, u. projyu = OD

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

Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,

Q: Find a vector a that has the same direction as (-10,7, 10) bưut has length 4.

A: In the given problem we have to find a vector a that has the same direction as -10, 7, 10 but has…

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: Show that the vectors are orthogonal.

A: Given : 3,6 and 4,-2

Q: Find the unit vectoru in the di rection of the vectorv=3(2, 2, 1).

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.