please find the augmented matrix for the following system of linear equations.

Question

3x1 - 2x2 = 18

 

4x1 + 5x2 = 1

 

7x1 + 3x2 = 19

Answer 1

the third equation is the sum of equations 1 and 3, then we can take this two eqwations as the ones that will give the solution. The set of equations will be:

3X1 - 2X2 = 18

4X1 + 5X2 = 1

The augmented matrix will be:

3  -2  18

4   5    1

 

solving for the determinant, the value is 15+8=23

solving for X1, the value is 18*5+2 = 92 then X1 = 92/23 = 4

solving in the same way for X2, the value is 3- 72 = -69, X2 = -69/23 = -3

Then check the two answers and  the three equations are oK even in the third equation the values fit.

CHECK!!!!!!!!!!!!!!!!!!!!!!!!!!!!