Write solution to system, if one exsist

Question

[ 1 0 2  | 5

  0  1 3 | 4

  0 0 0  | 1 ]

Answer 1

This is probably a good time for you to learn about the equivalence between augmented matrices and systems of linear equations.  The augmented matrix you have written is equivalent to the following system of 3 equations in 3 unknowns:  

 

1x + 0y + 2z = 5

0x + 1y + 3z = 4

0x + 0y + 0z = 1  

 

Look very carefully at the last equation.  Are the any values of x, y and z that will make that equation true?  If not, then there is no solution to the system you wrote.