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Example Question #1 : Augmented Matrices
Express this system of equations as an augmented matrix:
Arrange the equations into the form:
, where a,b,c,d are constants.
Then we have the system of equations: .
The augmented matrix is found by copying the constants into the respective rows and columns of a matrix.
The vertical line in the matrix is analogous to the = sign thus resulting in the following:
Example Question #1 : Solve A System Of Equations In Three Variables Using Augmented Matrices
Using an augmented matrix, solve the following system of equations:
Which of the following are the values of ,,and that satisfy this system?
Create an augmented matrix by entering the coefficients into one matrix and appending a vector to that matrix with the constants that the equations are equal to. Then you can row reduce to solve the system.
First, lets make this augmented matrix:
Now we can row reduce the matrix using the three row reduction operations: mutliply a row, add one row to another, swap row positions.
First, we can subtract .
You can stop here given that this augmented matrix can be rewritten as a system again with
, or you can continue using the matrix, subtracting multiples of from the other two rows to get an identity matrix yielding the solution to the system.