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 42AYU
Solution:
Consistent system, infinitely many solutions.
Explanation of Solution
Given:
Formula used:
To solve a system of two equations in and using matrices:
Step 1: Write the corresponding matrix associated with the system of equations.
Step 2: Use elementary row operations to get equivalent matrix of the form:
; where are constants.
Step 3: Solve for and .
Calculation:
The above equations can be rewritten as,
or
We find that both the given equations represent the same equation .
Here the number of variables is 2, whereas the number of equation is 1 (less than 2).
Therefore the given system is consistent and has infinitely many solutions.
Chapter 11 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
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