Consider the vectors ?? = (1,2,3), ?? = (3,2,9) ??? ?3 = (5,2, −1) ???? ?ℎ? ?????? ????? ?3.Determine ? = {?1,?2, ?3} is linearly dependent or independent. Q. No. 2(a) (2 x 1 = 2)PLO 1, CLO 2Consider the vectors V1 = (1,2,3), V2 = (3,2,9) and V1 = (5,2, –1) from the vector space R³.Determine S = {V1,V2, V3} is linearly dependent or independent.Q. No. 2(b) (3x1 = 3)PLO 1, CLO 2Solve the given linear system of equations by Gauss Jordan elimination method or row reduced echelon form.

A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Answered: Consider the vectors ?? = (1,2,3), ?? =…

Consider the vectors ?? = (1,2,3), ?? = (3,2,9) ??? ?3 = (5,2, −1) ???? ?ℎ? ?????? ????? ? 3 . Determine ? = {?1,?2, ?3} is linearly dependent or independent.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

See similar textbooks

Related questions

Q: Show that the vectors ?1 = ( 1, 1, 2, 4 ), ?2 = ( 2, -1, -5, 2 ), ?3 = ( 1, -1, -4, 0 ) and ?4 = (…

Q: Are the Following Vectors Linearly Dependent or Independent? 3) (0,1,0), (2,1,0), (3,4,7) Ans.…

Q: Are the vectors vl = (2, 0, -1), v2 = (4, 0, 7), and v3 = (-1, 1, 4) linearly independent in R3 ? a.…

A: If the linear combination has only trivial solution then all vectors are linearly independent

Q: Given the vectors ( 1 1 0), (0 2 3), (1 2 3), ( –1 0 3) in R3. Given vectors are linearly dependent.…

Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

Q: Which of the following vectors are linearly independent? O None of these O (2,1,1), (1,3,2),…

Q: Determine whether the vectors a = 2i − 3j + 5k, b = 3i + j − 2k and c = i − 7j + 12k are linearly…

A: We have to solve given problem:

Q: Are the following sets of vectors linearly independent? Show the details of your work. [3 4 0 1], [2…

Q: Determine whether the following vectors are linearly independent in R2:

A: According to the given information, it is required to determine whether the given vectors are…

Q: () (3) The vectors and are Select one: a. Linearly dependent b. Linearly independent

Q: Are the Following Vectors Linearly Dependent or Independent? 1) (3,4), (4,3) Ans. Independent

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

A: Given: Some pairs of vectors. To find: Which of the pairs are linearly independent. Linearly…

Q: 5. u = Write the linear combination of standard vectors i and j.

Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

Q: Which of the following vectors are linearly independent? Non of these O D O A O B

Q: Which of the following pairs of vectors are linearly independent? u= (1,2) and w = (-2,-4). u= (1,0)…

A: If an ordered pair (x,y) can be written as k(x,y) for k any integer.

Q: Are the following vectors linearly independent? ,, Do the following apply to give an answer? ?…

A: the given vectors, 4,0,0,, 5,-1,0,1,5,5

Q: Which of the following vectors are linearly independent? Non of these

A: We want to find independent vectors.

Q: 3 2 (c) 1 2 -2 -2 N NO

A: Question is solved.

Q: Which of the following sets of vectors in P2 are linearly dependent? (a) 2-x+4x?, 3+6x +2x², 2 + 10x…

A: (a) given set of vectors we shall write in matrix form A= 2-14362210-4if rank of above matrix is…

Q: Which of the following sets of vectors in R² is linearly dependent? A. {(1,0), (0, 1)} B. {(1,0),…

A: A set of vectors is said to be linearly independent if the matrix with these vectors as columns has…

Q: Use a counterexample to show that the following statement is false: if a, b and c are nonzero…

Q: Are the following vectors Linearly Independent? Show your work vų = [2 4 – 5], v2 = [7 2 – 1],v3 =…

A: Let x, y , z be three scalers. Condition for these vectors to be independent :

Q: 1) Determine whether the given vectors are linearly dependent or linearly independent. a)…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Which of the following sets of vectors in Rª are linearly dependent? (a) (3,8, 7, – 3). (1, 5, 3, –…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: Determine whether the following vectors are linearly independent in R2:

Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

Q: Are the following sets of vectors linearly independent? Show the details of your work. 17. [3 4 0…

A: We have Solve using row-echelon form

Q: 2 (6) (G) () 3. 4. 2 3 5. 1

A: Solve it.

Q: Find the value(s) of h for which the vectors are linearly dependent. [1 11:-5 -2 6.

A: To find the value of h for which the vectors are linearly dependent.

Q: Find the value of c for which the vectors -2 and c-3 in R'are linearly dependent. Select one: 1 2 O…

Q: Which of the following sets of vectors are linearly independent? ° {0 ( 2 3 -3 2 4 ° {() () } 5

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

Q: () () 1. 2.

Q: Which of the following collections of vectors are linearly independent in R3? (a) (1, 1, 1)T , (1,…

A: Vectors are said to be linearly independent when the determinant is not zero. a. Since the…

Q: Which of the following vectors are not linearly independent? Non of these

Q: Which of the following vectors are linearly independent? (2) (0) 21

Q: 1 1 -1 |1– 5k + k² 1+4k 1– 2k 3 -2 1

A: we can write the given vectors as a linear combination of vectors…

Q: Which of the following sets of vectors are linearly independent?

Q: Which of the following vectors are not linearly independent? 日L O B O A

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2> and w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0,…

Q: Find all real values of c such that the vectors [2 and +3 are linearly independent.

Q: })- The vectors and are Select one: a. Linearly dependent b. Linearly independent

Q: Which sets of vectors are linearly independent and which are not? 4 2 6. 9 0. 3. 2. 3. 2. 2. 1.

Q: Show that if u and v are linearly independent vectors, then so are u + v and u -v.

A: Given : u and v are linearly independent vectors. To prove : u + v and…

Q: Given vectors in R3 (2 -1 0),(3 1 2) and ( 1 0 1). They are linearly independent. Select one: O True…

Q: There are 6 linearly independent vectors in R°. O True False

A: We know that the dimension of the vector space R5 is 5.

Q: Q3: Are the following vectors linearly dependent or independent? 2) (1,4,5), (4,4,8), (3,–3,0)

A: We will check if the determinant of the matrix formed by the given vectors is zero or not.

Q: Are the Following Vectors Linearly Dependent or Independent? (3,-2,0,4),(5,0,0,1),(-6,1,0,1),…

A: Vectors v1, v2, v3,..........vn are linearly independent if for scalars c1, c2, c3,.........,cn such…

Q: Determine the following vectors in R3 ܴare either linearly dependent or linearly independent.…

A: We have to determine the following vectors in R3 ܴare either linearly dependent or linearly…

Concept explainers

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

100%

Consider the vectors ?? = (1,2,3), ?? = (3,2,9) ??? ?3 = (5,2, −1) ???? ?ℎ? ?????? ????? ?
3
.
Determine ? = {?1,?2, ?3} is linearly dependent or independent.

Q. No. 2(a) (2 x 1 = 2)
PLO 1, CLO 2
Consider the vectors V1 = (1,2,3), V2 = (3,2,9) and V1 = (5,2, –1) from the vector space R³.
Determine S = {V1,V2, V3} is linearly dependent or independent.
Q. No. 2(b) (3x1 = 3)
PLO 1, CLO 2
Solve the given linear system of equations by Gauss Jordan elimination method or row reduced echelon form.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Magnitude$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Define T:R2R2 by T(v)=projuv Where u is a fixed vector in R2. Show that the eigenvalues of A the standard matrix of T are 0 and 1.
Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.
Find a basis for R2 that includes the vector (2,2).
Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from R3 into R3 such that the set {T(v1),T(v2),T(v3)} is linearly dependent.
Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.