



 
Hi Mary, we hav two responses for you. I started with the matrix I first multiplied the first row by 1/3 to get Now multiply the first row by 2 and add it to the second row Can you complete it now? Hi Mary, An augmented matrix can be used to represent a system of equations. If we represent the two equations
as a matrix of the form
then the first column represents the x's, the second column the y's, and the last column a "constant". Since we can add and subtract equations which are part of the same system of equations, we can do First, subtract the second row from the first, and rewrite the matrix is transformed to:
That's what's called a row operation, an operation on a row of a matrix. The result was obtained by
Now let's subtract the first row from the second row:
What does this mean? if we write the rows of the matrix back out in their full form, we'll see that
That means that y = 0. You should now be able to complete the problem. The idea is to use row operations on an augmented matrix, which represents a system of equations, to reduce the system to a solvable form. In general, we want the matrix to be in "reduced rowechelon form". That means that the matrix looks like
for a 2x3 matrix, where A and B are any value. That would mean that x = A and y = B. If the equation is solvable, it is possible to get the matrix into rowechelon form by means of rowoperations. If you can't get it into row echelon form, either the system is unsolveable, like:
or the system has infinitely many solutions:
where A and B are not 0. Sometimes we don't have to go all the way to reduced row echelon form, as above. In your example, we only needed to perform a few rowoperations to get the system into a form which could be easily dealt with, by observing that y = 0. Using row operations on an augmented matrix to solve a system of equations is called the GaussJordan method. Hope this helps! Gabriel Potter  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 