Find the largest possible number of independent vectors among V2 V5 v6 = ustify your answer.

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

A:

Q: What is a vector?

A: A quantity that has magnitude as well as direction is called a vector.

Q: Find the largest possible number of independent vectors among 1 Vi = V2 V3 V4 Find any independent…

A:

Q: If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector?…

A: Explanation:

Q: What is the zero vector?

A: We have to define

Q: 26. Find the vector that has the same direction as (6, 2, -3) but has length 4.

A:

Q: Are the following vectors linearly independent? Yes No , ,,

A:

Q: Are the following vectors linearly independent? ,,

A:

Q: Find the largest linearly independent set of vectors from the list given below. V2 = vz = %3D

A:

Q: Dilate the vector (-3,5) by a factor of 3. ([ ? ],[])

A: Given vector: V=-3, 5 ……1   Also, Scalar factor is 3.

Q: Sketch the given vector with initial point (1, 6). u = (-7, -4)

A:

Q: Find a vector that has the same direction as [4, 2,5] but has length 35.

A:

Q: 5. 3 2 tu

A:

Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: We say that two vectors are equivalent .if they have the same components

A: Ginen statement, Two vectors are equivalent if  they have same component.

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: Two vectors are equivalent if they have the same _______ and _________.

A: Two vectors are equal if they have same magnitude and same direction. If we have a vector u=3i+4j…

Q: Express the product Ax as a linear combination of the column vectors of A. 2 3][3 -4 + 2 3 5 + 3 |…

A: To find out the correct option.

Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: 9. Explain why four vectors is R³ are always linearly dependent.

A:

Q: We define a median vector of a triangle to be the vector from a vertex of the triangle to the…

A: Let ,The triangle be ∆ABC A(x1, y1, z1)B(x2, y2, z2)C(x3, y3, z3)AM→ , BM→ , CM→ be the medians

Q: Find a vector in the same direction as (3, –2) with length 10.

A: The vector that has the same direction as 3,-2 has the coordinates proportional to the given vector.…

Q: Find the vector that has the same direction as (3, 2, -6) but has length 5.

A: Just follow the flow and you are done.

Q: Apply Gram- Sch maidt process to the vectors [ (7,

A:

Q: Find a vector that has the same direction as (-4, 6, 4) but has length 6.

A: we have to find a vector that the same direction as <-4, 6, 4> but has length 6

Q: Calculate the sum of the vectors that can be drawn as a vecto from the vertices of the triangle…

A: The vertices of the triangle is A7,4,-4, B1,-1,1 and C-8,-1,3

Q: Are the following vectors linearly independent? , ,

A: A set of vectors v1,v2,...,vk is linearly independent if the vector equation x1v1+x2v2+···+xkvk=0…

Q: Find the angle between the vectors (-8, 1) and (5, 4). Carry your intermediate computations to at…

A: Let, the given vectors     u→=-8,1,  v→=5,4we have to find the angle between the vectors.

Q: Sketch the given vector with initial point (7, 5). %3 (4, 2) u =

A:

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: Are the follovwing vectors linearly independent? ,,

A:

Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: Find the vector that has the same direction as (2, 6, -9) but has length 4.

A:

Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

A:

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

A: A vector is given

Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

A:

Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: What helps to set of vectors linearly independent?

A:

Q: Show thet direcion vectors of Tue Iae メ-3 レ り+ チ一て Laeメ-コ X-3 ソャ) Z-3 -2 are orthogohal

A: Direction vectors and orthogonality

Q: Find the largest possible number of independent vectors among 、H-E~目 V1 = V2 = V3 Find any…

A:

Q: Explain the Combination of basis vectors.

A:

Q: Find the area of a parallelogram with two sides identified by vectors from the origin to the points…

A:

Q: Find the angle between the vectors (-5, 4) and (-3, -1). Carry your intermediate computations to at…

A: Solution:

Q: Create a column vector with 14 equally spaced elements in which the first element is 3 and the last…

A: Arithmetic Progression:                          an=a1+n-1d where an= the nth term in the sequence…

Q: Calculate the first two vectors generated by the Gauss-Seidel method.

A: Gauss Seidle method

Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

A:

Q: Show that a set of vectors, which contains a set of linearly dependent vectors, is linearly…

A: To show that a set of vectors, which contains a set of linearly dependent vectors, is linearly…

Q: Express the product Ax as a linear combination of the column vectors of A. 1 21 3 + 3 +3 2.

A: The given product, A2×2x2×1=12-3432 Which will result into a vector of order 2×1

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.