Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. Choose the correct answer below. O A. The system is consistent because all the columns in the augmented matrix will have a pivot position. B. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix. O C. The system is consistent because the augmented matrix will contain a row of the form O .. 0 b with b nonzero. D. The system is consistent because the rightmost column of the augmented matrix is not a pivot column.

Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. Choose the correct answer below. O A. The system is consistent because all the columns in the augmented matrix will have a pivot position. B. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix. O C. The system is consistent because the augmented matrix will contain a row of the form O .. 0 b with b nonzero. D. The system is consistent because the rightmost column of the augmented matrix is not a pivot column.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Determine whether the statement is true or false. If a linear system has infinitely many solutions,…

Q: For each matrix below, determine the value(s) of h such that the corresponding matrix is the…

Q: Suppose a 4x8 coefficient matrix for a system has four pivot columns. Is the system consistent? Why…

Q: 0 2 1 0 502 0 0 43 1 , Exercise 16.

Q: Convert the given system to an augmented matrix. -2x15x210x3 x1 7x1 2 2x2 + 3x3 = -1 17x2 + 34x3 <=…

A: Step 1: Let's reduce the augmented matrix to echelon form:…

Q: (a.) 1 0 0 0 1 0 0 1 0 0 0 1 0 -1 3 (ь.) 1 -1 0 1 0 0 0 0 2 02 -2 03 0 1 1 0 0 5 (c.) -1 0 2 0 1 0 1…

A: a) The system is consistent x1=5 x2=-1 x3=3

Q: Find an equation involving g, h, and k that makes this augmented matrix correspond to a consistent…

Q: 1. Write the following matrix as a system of equations. Then use the matrix to solve the system. X…

A: Convert given agumented matrix into system of equations. Solve given augmented matrix by Gaussian…

Q: A certain system of 5 linear equations in 4 variables is known to have infinitely many solutions.…

A: We have to solve given problem:

Q: Consider a linear system whose augmented matrix is For what value of k will the system have no…

A: Consider the Augmented matrix .To Find:For what value of k will the system have no solution?

Q: The network diagram shown below, shows part of a shopping complex, with nodes A, B and C…

A: Given there are three stores A, B, C and the point of entry or exits E. The network diagram for the…

Q: The augmented matrix of a linear system has been reduced by row operations to the form shown.…

A: System of Simultaneous Linear Equations: Let us consider the following linear system of m equations…

Q: Given: 2a + 5b + 3c = 2 3a + b - 2c = 3 -a + 2b + c = 1 Instruction: Identify the coefficient…

Q: The augmented matrix of a linear system has been reduced by row operations to the form shown.…

Q: Let A be a matrix with linearly independent columns. Select the best statement. OA. The equation Ax…

A: Given that A is a matrix with linearly independent columns

Q: 9. 0 0 LO 0 0 1-3 0 1 -3 000 0 0-7 -1 4

A: In this question, we will solve the given augmented matrix and find the solution to the original…

Q: Suppose a 31 x 42 coefficient matrix for a linear system has thirty-one pivot columns. a. Is the…

Q: Find a system of linear equations that has the given matrix as its augmented matrix.

A: Given:Augmented matrix:1. Write the coefficients of the x-terms as the number down the first…

Q: Suppose a system of linear equations has a 3x5 augmented matrix whose fifth column is not a pivot…

A: Suppose a system of linear equations has a 3x5 augmented matrix whose fifth column is not a pivot…

Question

Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent.
Choose the correct answer below.
A. The system is consistent because all the columns in the augmented matrix will have a pivot position.
B. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix.
O C. The system is consistent because the augmented matrix will contain a row of the form
[ 0
O b with b nonzero.
...
O D. The system is consistent because the rightmost column of the augmented matrix is not a pivot column.

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 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Systems of Linear Equations$

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

Suppose each matrix below represents the augmented matrix for a system of linear equations. For matrices (a) and (b), determine if the system is consistent. If the system is consistent, determine if the solution is unique. (Note that leading entries marked with an X may have any nonzero value and starred entries ( * ) may have any value including zero.) a. b. 0 0 0 0 0 0 a. Select the correct answer below. A. The system is consistent, with infinitely many solutions. B. The system is inconsistent. OC. The consistency of the system and the number of solutions cannot be determined with the given information. O D. The system is consistent, with a unique solution. b. Select the correct answer below. O A. The system is consistent, with infinitely many solutions. O B. The system is consistent, with a unique solution. C. The system is inconsistent. O D. The consistency of the system and the number of solutions cannot be determined with the given information.
Suppose a matrix A has columns that span Rn. Select the best statement. O A. Then the equation Ax = 0 can have nontrivial solutions, but the shape of the matrix will not give us that information. O B. Then the equation Ax = 0 must have nontrivial solutions. O C. Then the equation Ax = 0 cannot have nontrivial solutions. D. Then the equation Ax = 0 will have nontrivial solutions precisely when it is not square. o E. Then the equation Ax = 0 will have nontrivial solutions only if one column is a multiple of another column. F. none of the above
4. Below is the augmented matrix of a system of linear equations. Using row operations, bring the matrix to reduced echelon form. List the basic variables and free variables. Then present the general solution of the system. :) 2 40 2 0 0 1 1 0 0 4 8040
Please help. Find the augmented matrix and all solutions of the following linear system. Thank you.
Solve b part
The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. *** 1 -1 0 0 -5 0 0 -6 1 -3 001-2 0001 2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The solution set is empty. ⒸB. The solution set contains one solution: (32 12.6.1) (Type integers or simplified fractions.) OC. The solution has infinitely many elements. 4