Quandaries
and Queries 

My name is Michael and I'm in the 11th grade. I have a Math question that I can't solve. The problem is system of equations that I need to do in augmented matrix form, find the row echelon form, and solve it by using back substitution.
Please respond. Thank you! 

Hi Michael, There are many ways to arrive at a row echelon form. I try do do as much as I can without introducing fractions. Multiply the first row by 1 and add it to the second row and then multiply the first row by 2 and add it to the third row. Hence
becomes
Now multiply the second row by 1 and add it to the third row and then multiply the second row by 2 and add it to the first row. The matrix then becomes
Next multiply the third row by 2 and add it to the first row to get
Multiply the first row by 2 and add to the third row to get
Finally interchange the first and second rows and multiply the third row by 87 to get the row echilon form
Thus z = 3. Back substitute to get y and x and then VERIFY that you have the correct solution. Penny 

