Answered: Determine whether the set S is linearly…

Determine whether the set S is linearly independent or linearly dependent. S = {(7, 0, 0), (0, 9, 0), (0, 0, −16), (7, 5,−8)}

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 73E: Proof Let S={u,v} be a linearly independent set. Prove that the set {u+v,uv} is linearly...

See similar textbooks

Related questions

Q: Determine whether the set S is linearly independent or linearly dependent.S = {(1, 0, 0), (0, 4, 0),…

A: We can write (1,5,-3) as:

Q: Which of the following sets in R is linearly dependent? 36- OA {(2,0, 1), (0,4, -1), (0, 5, 1)}…

Q: Determine whether the set S=(U,V,W) are linearly independent or linearly dependent. Where, U=…

Q: Let 2 v = w = and 0 = 3 Which of the following sets are linearly dependent? Select all that apply.…

A: Solution:Given vectors are v→=203 , w→=111 , 0→=000

Q: Determine if b is a linear combination of a1, a2, and a3 a1 a2 a3 b 1 -2 -6 11 0 3 7 -5 1…

A: It is given that b is a linear combination of a1, a2, and a3.

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(1, 2), (5, 3)} O…

Q: Determine all values of c so that the set {t +3, 2t +c2+2} is linearly independent.

A: Given: The set t + 3, 2t + c2 + 2 is linearly independent. To determine all values of…

Q: Determine whether the set S is linearly independent or linearly dependent. S={(2, 1, 6), (3, 2, -1)}…

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(-5, -2, 4), (2, -1,…

Q: b = Find whether {a, b} linearly independent or not. 5. Let a are

A: Given a = 20 , b = 07

Q: Determine whether the set S is linearly independent or linearly dependent.S = {(3, −6), (−1, 2)}

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(-6, -2,4), (3, -3,…

Q: Which of the following sets is linearly independent? O M={ (1,0,1 ),(3,0,3),(0,0,0) } O M={…

Q: Q4) Determine whether the set S is linearly independent or linearly dependent a) S = {(2,1,–2), (–2,…

A: We have to check whether the set S is linearly independent or linearly dependent.

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(-5, -1, 6), (1, –1,…

A: Explanation of the answer is as follows

Q: S Let v1 = ,and v3 = 1 for which values of S, V1, V2 , and v3 are linearly S independent. Select…

A: Linear Combination: Let V be a vector space over the scalar field F. Let x1, x2, ..., xn be vectors…

Q: Determine whether the set S is linearly independent or linearly dependent S = {(1, 0, 0, 0), (1, 0,…

A: NOTE: Refresh your page if you can't see any equations. . write all 4 vectors in the matrix

Q: a 6) Determine the value(s) of a such that is linearly independent. a +

A: Let us consider the n vectors of order 1x n in Rn The vectors are said to linearly dependent if the…

Q: Let B {(1,2,3), (3, 2, 1), (0,0, 1)}. Show that B is linearly independent and spans R. Show all of…

A: In this question, concept of linear span is used. Linear spanLet V represent a vector space, and…

Q: Determine whether the set S is linearly independent or linearly dependent.S = {(0, 0), (1, −1)}

A: Given:

Q: Which of the following sets is linearly independent? * O M=((1,0,1),(3,0,3),(0,0,0) } O M=(…

Q: (a) {(1,0,0), (5,5, 0), (3, 3, 3)} (b) {(2,5,4), (–2, 1, 0)} (c) {(-3,2,1), (0, 0, 0) , (1, 2, –3)}…

Q: The functions Inx and Inx are linearly independent functions.

A: two functions are y1=lnx, y2=lnx3 find its derivative y1'=ddxlnx, y2'=ddxlnx3 y1'=1x,…

Q: Which of the following sets are Linearly independent? M={(1,1,0), (0,1,0), (1,0,1)} M={ (1,2),(3,…

A: If one vector can be expressed as a linear combination of other vectors , then the set of vectors…

Q: Find all values of h such that {t² + 2,5t² + t - 7,-4t² - t + h} is a linearly dependent set in…

A: We are given a set of 3 polynomials in polynomial space P2[t] , including a unknown parameter h And…

Q: 2. Let -2 and a (a) Check whether u and v are linearly independent or not. (b) Check whether w is a…

Q: Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1,…

Q: (e) Determine whether or not the rows of A are linearly independent. O independent O dependent (F)…

A: The given matrices are: A=-2-580-1713-515-5-11173-5317-135-3B=1010101-2030001-500000

Q: Which of the following sets is linearly independent? * O M={(1,3,4),(1,2,5),(-1,0,-2)} O M={(1,1…

Q: Which of the following sets is linearly independent? * T2 21 3. 81 3 the above set O the above set…

A: For a 2×2 matrix abcd, if detabcd=0, then matrix is linearly dependent, otherwise linearly…

Q: For which values of C is the set C linearly dependent? 3. C = -1, 2 C=-1,-2 C=1,-2 C= - 1, 1 O c=1,…

Q: Which of the following sets is linearly independent in IR3 ? O (0,1,1), (0,-2,-2), (0,3,3))…

A: Please see the below picture for detailed solution.

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(0, 0, 0, 1), (1, 0,…

A: We determine whether the set S is linearly independent or linearly dependent.

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(-6, -1, 6), (3, -1,…

Q: 0. Let v is v linearly independent or dependent? O Independent O Dependent

A: 1. We use the property of determinants to answer the given question. 2. We use the definition of…

Q: Determine whether the set S'is linearly independent or linearly independent. S = {(3, –6),(-1, 2)} O…

Q: Which of the following sets are Linearly independent? None of these O M={(1,1,0), (0,1,0), (1,0,1)}…

A: Let M = { (1, 1, 0), (0, 1, 0), (1, 0, 1) } Let a, b, c are three scalar such that a(1, 1,…

Q: Which set of functions which is not linearly independent is A-X^2,4x^3 B-2x,6x+3,3x+2 C-e^x,e^2x…

A: A set of functions will be linearly independent if there Wronskian is not equal to zero. Wronskian…

Q: a 6) Determine the value(s) of a such that is linearly independent.

A: Given the set 1a,aa+2 is linearly independent.

Q: Which of the following sets is linearly independent?* O M-((1,0,1),(3,0,3), (0, 0, 0) } M=((1,1,3),…

A: Since it is a multiple question. As per our company guidelines we have to solve the first question.…

Q: S = {(6,2, 1), (-1,3, 2)} is: a. a linearly independent set of R b. a linearly dependent set of R.

A: First we make the linear combination of the given vector, then we check the set is linearly…

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(2, 3), (3, 4)}…

A: Given S=2, 3, 3,4

Q: Let ty Fir what value(s) of h is the set (vy,, t) linearly dependent? A. h 0 B. All h C. h=-10 D.…

A: If the set v1, v2, v3 is linearly dependent then, αv1+βv2=v3

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(0, 0, 0, 1), (0, 0,…

Q: Which of the following sets is linearly independent? M=( (1,2),(2,4), (-1,2)} M=((1,0,1),(3,0,3),…

A: M=1,2,2,4,-1,2 As 2,4=21,2+0-1,2 which means 2,4 can be written as linear combination of 1,2, -1,2…

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(1, 0, 0, 0), (1, 0,…

Q: Which of the following set S is a linearly independent? a. S = ((0, 0), (1, 2)} b. S = {(1, 2), (2,…

A: We have to show that which set is linearly independent. A linearly independent set is the set which…

Q: Determine whether the set S is linearly independent or linearly dependent. S- {(-4, -3, 5), (2, -2,…

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(−2, 1, 4), (1, 8,…

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

Determine whether the set S is linearly independent or linearly dependent.

S = {(7, 0, 0), (0, 9, 0), (0, 0, −16), (7, 5,−8)}

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 2 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, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

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)
Proof Let S={u,v} be a linearly independent set. Prove that the set {u+v,uv} is linearly independent.
Review Exercises Writing a Linear Combination In Exercises 9-12, write v as a linear combination of u1,u2 and u3, if possible. v=(3,0,6),u1=(1,1,2),u2=(2,4,2) and u3=(1,2,4)
Market supply The following table shows the quantity S of wheat, in billions of bushels, that wheat supplies are willing to produce in a year and offer for sale at a price P, in dollars per bushel. S = quantity of wheat P = price 1.0 1.35 1.5 2.40 2.0 3.45 2.5 4.50 In economics, it is customary to plot S on the horizontal axis and P on the vertical axis, so we will think of S as a variable and of P as a function of S. a. Show that these data can be modeled by a linear function, and find its formula. b. Make a graph of the linear formula you found in part a. This is called the market supply curve. c. Explain why the market supply curve should be increasing. Hint: Think about what should happen when the price increases. d. How much wheat would suppliers be willing to produce in a year and offer for sale at a price of 3.90 per bushel?