Concept explainers
In problems 39-74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
To find: The solution to the given system of equations using matrices.
Answer to Problem 68AYU
Solution:
Consistent system, infinitely many solutions.
Explanation of Solution
Given:
Calculation:
To solve a system of three equations in and using matrices:
Step1: Write the corresponding matrix associated with the system of equations.
Step2: Use elementary row operations to get equivalent matrix of the form:
; where are constants.
Step3: Solve for and .
The rank of coefficient matrix and augmented matrix are both equal to 2, which is less than 3.
Here the number of variables is 3, whereas the number of equations is 2.
Since the number of equations is less than the number of variables, therefore the given system of equations is consistent and has infinitely many solutions.
Chapter 11 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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