Question: If a vector B is a linear combination of the columns of A, show that the system AX = B is consistent (that is, it

If a vector B is a linear combination of the columns of A, show that the system AX = B is consistent (that is, it has at least one solution.)

Step by Step Solution

★★★★★

3.32 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Write A a 1 A 2 a n where ai is column i o... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

950-M-L-A-L-S (6200).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Show that the 7th column of the matrix product AS is a linear combination of the columns of A with coefficients the entries in bj, the jth column of B.

Q:

Write each of the following linear systems as a linear combination of the columns of the coefficient matrix: (a) 3x1 + 2x2 + x3 = 4 x1 - x2 + 4x3 = -2 (b) -x1 + x2 = 3 2x1 - x2 = -2 3x1 + x2 =1

Q:

In Exercises 1-3, determine if the vector v is a linear combination of the remaining vectors. 1. 2. 3. 1 LI 2 1 2 LI 2 011 110 123

Q:

Algebra (1 point) Which of the following statements are true? DA If the columns of an m x n matrix A span R", then the equation Ax = b is consistent for each bin R". B. Every matrix equation Ax = b...

Q:

please provide detailed steps on how I can go about solving this problem. Thank you. 012 3 2 W_[W Jew. s. (12 pt) Express the vector b as a linear combination of the columns in, v2, v3, v4 of the...

Q:

Mark each statement True or False (T/F). Justify each answer. (T/F) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.

Q:

1. Describe the possible echelon forms of a nonzero 2 x 2 matrix. (3 Select all that apply. (Note that leading entries marked with a I may have any nonzero value and starred entries ( * ) may have...

Q:

Answer the questions below relating to linear algebra (three parts). Please make sure to easily/accurately answer all the question parts. Find the general solution of the system whose augmented...

Q:

math 79 linear algebra mework Question 1, 1.3.1 HW Score: 0%, 0 of 25 points Save Part 1 of 2 O Points: 0 of 1 Compute u + v and u - 2v. u+ v= (Simplify your answer.)HW Score: 0%, 0 of 25 points Save...

Q:

please answer the questions below they are for linear algebra 1 E. . A matrix vector product is A linear system is consistent if and only ifthe last column of the augmented matrix does not contain a...

Q:

Describe the externality that arises from plastic bags. Draw a graph to illustrate how plastic bags create deadweight loss. Thin plastic shopping bags arent biodegradable. Americans use about 110...

Q:

Allotastock, Inc. (or A) is a corporation that engages in business and also owns stock in various other corporations. On January 1, 2018, As stock holdings are as follows: A holds 85,132 common...

Q:

9.29 Let us define S 2 = n i=1 (Xi X )2/n. Show that E(S 2) = [(n 1)/n]2 , and hence S 2 is a biased estimator for 2 .

Q:

To close the recessionary gap and achieve fullemployment real GDP as shown in Exhibit 9, the government should increase spending by a. $1 trillion. b. $1.2 trillion. c. $2.0 trillion. d. $2.5...

Q:

Given x,=(1, 1, 1)T and x2 = (3, - 1, 4)T: (a) Do x1 and x2 span R3? Explain. (b) Let x3 be a third vector in R3 and set X = (x1, x2, x3). What condition(s) would X have to satisfy in order for x1,...

Q:

Let a1 and a2 be linearly independent vectors in R3, and let x be a vector in R2. (a) Describe geometrically Span(a1, a2). (b) If A = (a1, a2) and b = Ax, then what is the dimension of Span(a1, a2,...

Q:

Let E = [u1, un] and F = [v1,..., vn] be two ordered bases for Rn and set U = (u1,..., un), V = (v1,...,vn) Show that the transition matrix from E to F can be determined by calculating the reduced...

Q:

Central Mass Ambulance Service can purchase a new ambulance for $200,000 that will provide an aumual net cash flow of $50.000 per year for five years, Calculate the NPV of the ambolance if the...

Q:

Can someone help me understand how to do this Here, you will make use of some statistical functions to determine critical values for distributions. Unless otherwise indicated, give all answers to at...

Q:

please help!!! The marginal revenue for a product is give by MR = 440 - 10x and the marginal cost is given by MC = 200+6x The cost of producing 10 units is $3300. Find the profit or loss of selling...