
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 47AYU
Solution:
Consistent system.
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 matrix associated with the above system of equations is:
The element in (row1, column1) position is already 1.
To get the (row2, column1) position as zero, multiply row1 by and add to row2:
Simplify:
To get the (row2, column2) position as 1, divide row2 by 2:
Simplify further:
Now the (row3, column1) position is already zero.
To get the (row3, column 2) position as zero, multiply row2 by and add to row3:
Simplify further:
To get the (row3, column3) position as 1, divide row3 by 4:
Simplify:
The above matrix corresponds to the system of equations:
Now substitute in the second equation , to get the value of .
Now substitute in the first equation , to get the value of .
Thus the solutions to the given system of equations are: .
Chapter 11 Solutions
Precalculus
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