Question

# Consider the system of equations, where h and k are real numbers.

x_{1} + 2x_{2 }

= 3

-2x_{1 }- x_{2 }+ 6x_{3 }= 6

3x_{2} + hx_{3 }= k

Write the system as an augmented matrix. I know how to write this as an augmented matrix if the coefficients and the constants are all numbers, but I don't know how to treat the "h" and "k." Please explain.

Row reduce the matrix to echelon form.

For what values of h and v does the system have no solution? a unique solution? infinitely many solutions? I have the impression that h and v have no solution if the equations are parallel lines, but I don't understand how to express this as h and v values.

Thanks.