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Solution to Problem4


*****

Problem4:

Find the solution to the system of equations with augmented matrix given by,

> ;

                           [1    0    0    -7     8]
                           [                       ]
                           [0    1    0     3     2]
                           [                       ]
                           [0    0    1     1    -5]


SOLUTION:


Assume the unknowns are (w,x,y,z). Start from the last row working upwards. The last equation is,

> Eq3 := y+z = -5;

                               Eq3 := y + z = -5

from where we get that

> y := -5 -z:

The second equation is,

> Eq2 := x + 3* z = 2;

                              Eq2 := x + 3 z = 2

from where we obtain that,

> x := 2 - 3*z:

finally the first equation is,

> Eq1 := w - 7*z = 8;

                              Eq1 := w - 7 z = 8

from where we obtain that,

> w := 8 + 7*z:

so there are infinitely many solutions to the system. All the points on the straight line

> {[w,x,y,z]};

                        {[8 + 7 z, 2 - 3 z, -5 - z, z]}

where z is an arbitrary scalar.

Ofcourse there are faster ways to get this answer with maple... here is one line solution,

> backsub(matrix(3,5,[1,0,0,-7,8, 0,1,0,3,2, 0,0,1,1,-5]));

                 [8 + 7 _t[1], 2 - 3 _t[1], -5 - _t[1], _t[1]]

_t[1] is maple funny way (to make sure the name is not being used by you) of writing the free scalar parameter z


Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Tue Feb 8 17:23:15 EST 2000