Concept explainers
To find: The solution to the given system of equations using matrices.
Answer to Problem 54AYU
Solution:
Consistent system of equations, infinitely many solutions.
Explanation of Solution
Given:
Formula used:
To solve a system of three 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 corresponding augmented matrix is:
Now we see that the rank of the coefficient matrix is 2, and the rank of augmented matrix is also 2, which is less than 3.
Since rank of the coefficient matrix and the rank of augmented matrix are equal and is less than 3, therefore the given system of equations has infinitely many solutions.
Hence this is a consistent system.
Chapter 11 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus: Early Transcendentals (2nd Edition)
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