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

x1 + 2x2

= 3

-2x1 - x2 + 6x3 = 6

3x2 + hx3 = 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.


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