Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![The image shows a matrix in row-echelon form, followed by a question asking for the final solution.
Matrix:
\[
\begin{bmatrix}
1 & 0 & 5 & | & 12 \\
0 & 1 & -7 & | & 0 \\
0 & 0 & 0 & | & 3 \\
\end{bmatrix}
\]
Explanation:
- The matrix represents a system of linear equations.
- The left part of the matrix (before the dashed line) is the coefficient matrix, and the right part (after the dashed line) is the constants from the equations.
- The third row shows all zeros to the left of the dashed line and a 3 on the right, indicating the system is inconsistent (contradictory), as there is no valid solution for the third equation.
Question:
"What is the final solution?" with a blank line for the answer.
Given this information, the correct understanding is that the system has no solution due to the inconsistency represented by the bottom row.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4a6764b-ec66-4cf8-9984-52f9ddecdfb1%2F4c557315-1904-4875-9825-d05f4bdc4716%2Fx6weevy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a matrix in row-echelon form, followed by a question asking for the final solution.
Matrix:
\[
\begin{bmatrix}
1 & 0 & 5 & | & 12 \\
0 & 1 & -7 & | & 0 \\
0 & 0 & 0 & | & 3 \\
\end{bmatrix}
\]
Explanation:
- The matrix represents a system of linear equations.
- The left part of the matrix (before the dashed line) is the coefficient matrix, and the right part (after the dashed line) is the constants from the equations.
- The third row shows all zeros to the left of the dashed line and a 3 on the right, indicating the system is inconsistent (contradictory), as there is no valid solution for the third equation.
Question:
"What is the final solution?" with a blank line for the answer.
Given this information, the correct understanding is that the system has no solution due to the inconsistency represented by the bottom row.
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