Matrices

The matrix is a way of changing equations with variables into a form where nunbers are listed in boxes that can be manipulated for the values of variables. A matrix is called by the number of rows times the number of columns. for example,  a matrix with 2 rows and 5 columns will be called (5x2). The three ways that matrix rows can be manipulated are:

1) interchange rows

2) add a row to another row

3) multiply or divide a row by a constant

The main goal of the Gaussian way is to get zeros below a diagonal of ones that start from the top left corner and end in the bottom right corner. Then, you create equations from the numbers you have and use back substitution into each equation to gain the values of each variable. However, in the Gaussian methods, zeroes are wanted everywhere except in the aforementioned diagonal. With the Gaussian, there is no need to find or use equations and substitution. all you need to do is state the value of each variable from interpreting the matrix.

The example shown online was wrong because he/she forgot to add the value of the last row in both of the steps. The line does not divide where the addition of subtraction can occur. Below are examples my group did: