Question

Which of the following statements accurately describes the system represented by the matrix $\left[\begin{array}{rrr|r}{1} & {5} & {-2} & {3} \\ {0} & {1} & {3} & {-2} \\ {0} & {0} & {0} & {5}\end{array}\right] ?$ (a) The system has one solution. (b) The system has infinitely many solutions. (c) The system has no solution. (d) The number of solutions cannot be determined.

Name: Problem 6, Chapter 8: College Algebra
Uploaded: 2020-05-16T21:18:13-08:00
Duration: 56 s
Channel: Santana Scott
Description: Which of the following statements accurately describes the system represented by the matrix [ 1 5 -2 3 0 1 3 -2 0 0 0 5 ] ? (a) The system has one solution. (b) The system has infinitely many solutions. (c) The system has no solution. (d) The number of solutions cannot be determined.

   Which of the following statements accurately describes the system represented by the matrix $\left[\begin{array}{rrr|r}{1} & {5} & {-2} & {3} \\ {0} & {1} & {3} & {-2} \\ {0} & {0} & {0} & {5}\end{array}\right] ?$
(a) The system has one solution.
(b) The system has infinitely many solutions.
(c) The system has no solution.
(d) The number of solutions cannot be determined.

College Algebra

Michael Sullivan 10th Edition

Chapter 8, Problem 6

Instant Answer

Solved by Expert Santana Scott

05/16/2020

Step 1

The matrix is in row-echelon form, which makes it easier to determine the number of solutions. Show more…

Show all steps

Thanks for your feedback!

Which of the following statements accurately describes the system represented by the matrix $\left[\begin{array}{rrr|r}{1} & {5} & {-2} & {3} \\ {0} & {1} & {3} & {-2} \\ {0} & {0} & {0} & {5}\end{array}\right] ?$ (a) The system has one solution. (b) The system has infinitely many solutions. (c) The system has no solution. (d) The number of solutions cannot be determined.

Play audio

Feedback

Santana Scott and 92 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Augmented Matrix Representation

An augmented matrix is a compact form used to represent a system of linear equations where the coefficients of the variables and the constant terms are combined into a single matrix. This form facilitates the application of matrix operations to determine the solution set of the system.

Row Echelon Form

Row echelon form is a simplified version of a matrix achieved by applying elementary row operations. It is useful because it makes the structure of the system more apparent, such as the positions of leading coefficients and potential zero rows, which are key to determining the nature of the solutions.

Inconsistency in Linear Systems

A linear system is inconsistent when one of the rows in its row echelon form shows a contradiction, such as all zero coefficients with a non-zero constant term. This indicates that no set of variable values can satisfy the system, meaning the system has no solution.

Please give Ace some feedback