solve using matrices and convert the matrix to reduced row echelon form

Question

6x+5y=9

x-3y= -10

Answer 1

The equations are 6x + 5y  = 9 and x - 3y = - 10

Write the equations into matrices form AX  = B .

A  is Coefficient matrix , X  is variable matrix and B  is Constant matrix.

A rectangular matrix is in row echelon form if it has following three properties.

• The first non zero element inb each row , called the leading entry is 1.
• Each leading entry is in a column to the right of the leading entry in previous row.
• Rows with all zero elements ,if any are below having non zero element .

The augment matrix is

Here represents first row and represents second row.

This matrix is now in row echelon form.

Solution x  =  -1 and y  = 3.