where m is a parameter.
Enter the following matrix
{ {M 1 -2} { M 'M-1' 2 } }
and type the ENTER key to have a copy,
then type rref, you get at level 1:
{ { '-M^2+2*M' 0 '2*M' } { 0 '2-M' -4 } }.
This means that:
This is the case iff all the coefficients in the list at level 2 are
non 0. You should have at level 2:
{ -1 'M+-2'
The second coefficient vanishes if m=2. You have to solve for this
particular case again. Recall the original matrix from the
stack and type:
'M=2' EXEC
This replace all occurences of M by 2 in the original matrix.
Now type rref again, you get:
{ { 2 1 -2 } { 0 0 4 }
The last line means that:
which is clearly impossible, the system has no solution.
If you have MATR installed, you can solve the system using the
RED instruction. Put the MATRIX on the stack, type
the list of unknown followed by -1 (+1 means that the constant
row is before the = sign, -1 means after the
= sign):
{ X Y -1}
then hit the RED menu key and SYST, you get the solutions
(value tagged by the corresponding unknown). At level 2, you get the list
of cases for which you need a specific study:
{ 'M^2-2*M' '-M+2' -1 'M+-2'
This means that we have to solve again for m=0 and m=2.
For systems, the SOLG menu key provide another way of writing
the solution as an affine space of solutions.
Recall the matrix on the stack (simply hit MATRIX), type:
'M=0' EXEC EVAL
and RED SOLG, you get at level 1:
If { }, { X Y }=:{ X -2 }
This means that (x,-2) is solution for every x. The If
statement shows necessary conditions for the system to have solutions
(here no condition, but if we try m=2 instead of m=0 the system
has no solution: the If statement is If { '0=-1'} never
fulfilled).
