Which of the following vectors are linearly independent? A) [1 2 3] [4 5 6] [7 8 9] B) [2 2 -1] [4 0 2] [0 6 -1] C) [1 2 3] [2 4 6] [3 4 5] D) [1 3 -2] [4 7 1] [3 -1 12] E) [1 2 1] [9 5 2] F) [3 5 2] [1 7 6] 12 5 31 G) [2 5 2] [1 6 6] [4 H) [-9 5 2] [1 -5 6] [2 5 -91 17 1 ol 10 41

Which of the following vectors are linearly independent? A) [1 2 3] [4 5 6] [7 8 9] B) [2 2 -1] [4 0 2] [0 6 -1] C) [1 2 3] [2 4 6] [3 4 5] D) [1 3 -2] [4 7 1] [3 -1 12] E) [1 2 1] [9 5 2] F) [3 5 2] [1 7 6] 12 5 31 G) [2 5 2] [1 6 6] [4 H) [-9 5 2] [1 -5 6] [2 5 -91 17 1 ol 10 41

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.1: The Geometry And Algebra Of Vectors

Problem 2EQ

See similar textbooks

Related questions

Q: Determine the dot products of the following pairs of vectors. (a) (3, 5), (3, -4) (b) (2, -5, 3),…

A: Solution :-

Q: Express EC by combinations of the vectors a, b and 7.

A: We have to write EC vector in terms of a,b and c

Q: linear Consider the following vectors in R³: V= (-1,7,2), u₁₁ = (1,3,5) U1₂ = (2₁-1₁3), (13=…

Q: 10 -00-0 7 12 5 -8- Are the vectors 6 and linearly independent? Explain! 8

Q: 1 4 7 Determine whether the set of vectors 2 3 6 9 is linearly dependent or not. If so, find a way…

Q: 4. Find 3v - 3u using the following vectors: u =

Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

Q: AB, BC, AC.

Q: Which of the following pairs of vectors are perpendicular to each other? a) (4, 14, -18) and (6, 21,…

Q: Consider the following vectors: 3 9 -6 6. b= -9 9 3. 10 -9 For each of the following vectors,…

A: Solution

Q: 5. Determine which sets of vectors are orthogonal. (a) 1 ↑ 1 0 -5 2 1 5 -309 (b) -4 2

Q: Let a (6,7, –2) and b = (4, 4, –1) be vectors. Compute the following vectors. A. a + b =( 10 11 -3…

Q: Which of the following sets of vectors are linearly independent? A. (4, 8,-5), (-9, -4, -6), (-13,…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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

Q: 1. Find A-C|(B – D) using the following vectors: A= C= D=

Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

Q: "Given that 3 -4 = 5 -3+ 2 5 ܐ write 3 as a linear combination of the vectors -2 + 5 -3 -2 5 -4 1 2…

A: Here , a vector is given and now we have to represent it as a linear combination of three vectors .

Q: 1) Determine if the vector b can be written as a linear combination of the vectors a₁, az, and al 1…

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

Q: a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express…

A: a. To express each column vector of AB as a linear combination of the column vectors of A, we can…

Q: -3 -3 9. 2 Let A = -3 -6 12 and b = 3 -3 -2 13 -5 Denote the columns of A by a1, a2, a3, and let W =…

Q: What is the value of each of the constants that are part of the linear combination between the…

Q: 1 3 a) Consider a set of vectors, x = |3 |,y = | 2 and z = L4 Can we express the vector, v = 4 as a…

A: The solution is given as

Q: 5: The vectors v = [1 2 9] and w= [2 4 18] are linearly independent vectors. O True O False

A: We will find the given two vectors are linearly independent is true or false in the following step.

Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

Q: a, b and c are three vectors in the third dimension with the following properties: a × b does not…

Concept explainers

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.

Question

Which of the following vectors are linearly independent?
A) [1 2 3]
[4 5 6]
[7 8 9]
B) [2 2 -1]
[4 0 2]
[0 6 -1]
C) [1 2 3]
[2 4 6]
[3 4 5]
D) [1 3 -2]
[4 7 1]
[3 -1
12]
E) [1 2 1]
[9 5 2]
F) [3 5 2]
[1 7 6]
[2 5 31
G) [2 5 2]
[1 6 6]
[4
H) [-9 5 2]
[1 -5 6]
12 5 -91
17
1
ol
10 41

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

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

Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)
Find a basis for R2 that includes the vector (2,2).
We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to the Irish mathematician William Rowan Hamilton. Hamilton considered his greatest achievement to be the discovery of qualernions, which he (incorrectly) predicted would revolutionize physics. Research the subject of quaternions. What are they? Why did quaternions fail to be as useful for physics as Hamilton predicted? How are quaternions useful, instead, for 3.D computer graphics? Write a paragraph or two about your findings.
Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)
7. Show that the vectors A=4a, -2a, +2a, and B = -6ā, +3ā, -3ā, are parallel to each other.
se. Justify_your answer 1 1 1 1 -1 is a linear combination of the vectors y,= 2 -1 V3= Show whether or not the vector V = ,V2= -1 -2 1 -1 Attach File Browse Mv Computer
2) Determine if the vectors are Linearly Independent or Linearly Dependent. - 5 -2 =2x(2) -3 x3) -(3) – 13] 4
Determine whether the following three vectors lie on the same line in R3: и, 3 (4,6,8), и, - (2,3,4), и, 3(-2, -3, - 4), (The End)
1. Suppose a and bare vectors such that a x b = (1, 0, 2). What is bx -2a *x (-2a² a. (-2, 0, -4) c. (1, 0, 2) d. (-4, 0, -2) b. (2,0,4)
If possible, find a linear combination of the form w = a₁v₁ + a₂₂ + 3⁄³ where v₁ = (2, −1, 4), v₂ = (3, 0, 1), v3 = (1, 2, −1), and w = (-7, 1, 5). (Give a, a, and a3 as real numbers. If w cannot be written as a linear combination of the other three vectors, enter DNE.) (₁₁²₂₁²3) =
Determine by inspection the linearly independent vectors O a. O b. O c. -8 12 -4 2 -3 5][2] Ú'Ì 8) 4 6 -3 9
3) Check whether the vectors V, = [1 3 3 5.V, =[3 10 6 7], V, = [2 7 3 21 are linearly independent.