I'm guessing you are using the essentials textbook. They have quite a few matrices questions that aren't actually in the course.
To answer your more general question about infinite and no solutions (I will not explain why, but will explain how to find them, because knowing 'why' is beyond 'methods'
) :
For infinite solutions, the equations are 'linearly dependant', that is,
, where
are real constants and eq1, eq2 and etc are equations.
That is, each set of coefficients (i.e. coefficients of x, coefficients of y, coefficients of z, constant term on RHS) must all follow this pattern. Solving this (see post above) will give you infinite solutions.
For singular solutions, use the rref function. For the above case, do
 & 13 \\ 10 & 8 & a-4 & 26 \\ \end{array} \right] \right))
The result will yield
Where x=k, y=m, z=n (for a given value of a, which gets substituted into the expression for k, m and n)
For no solutions, you try to find values of the variable such that k, m and n do not exist. In this case, k, m and n all have a common denominator of
, that is, if a=2, then you will be dividing by zero
undefined. Hence if a=2, there are no solutions.
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