Concept explainers
To find: The solution to the given system of equations using matrices.
Answer to Problem 65AYU
Solution:
Consistent system, infinitely many solutions.
Explanation of Solution
Given:
Calculation:
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 .
The corresponding matrix associated with the above system of equations is:
We see that the rank of the coefficient matrix is 2 and rank of augmented matrix is also 2; whereas the number of variables and the number of equations are both 3.
Since the rank of coefficient matrix and the rank of augmented matrix are both equal to 2, which is less than 3; the given system of equations is consistent and has infinitely many solutions.
Chapter 11 Solutions
Precalculus Enhanced with Graphing Utilities
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