Math CentralQuandaries & Queries


Question from Beth, a student:

I am having troubles finding this augmented matrix. I know how to do it but every time i do it it get a different answer and its not the right answer. Could you help me to make sure I do it right?

Here is the problem:
4x - 3y = 5
2x +9y = 6

thank you very much.

Hi Beth,

To form the augmented matrix you start with the matrix of coefficients

mtrix of coefficients

and augment it, or make it larger, by appending a column containing the right side of the equations

augmented matrix

At this point you need to use row operations to solve the original equations. There are many choices for row operations but one of my goals is to put off using fractions as long as possible. This is just to reduce the chance that I make arithmetic errors. Here is what I did

Interchange the two rows.

row op 1

Add -2 times the first row to the second row.

row op 2

Divide the second row by -7.

row op 3

Add -3 times the second row to the first row.

row op 4

Now I'm forced to use fractions. Divide the first row by 2 and the second row by 3.

row op 5

Now I can see that x = 3/2 and y = 1/3.

At this point you should verify that my answer is correct. I suggest also that yo try different row operations and see if you get the same answer.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS