Mathematica
Tutor
Part
10: Row operations on matrices
- Unassign
your variables again, and ask Mathematica to solve
|
x
+ 4y + 3z = 10
|
|
2x
+ y - z = -1
|
|
3x
- y - 4z = 11
|
- What
happens in Step 1? What do you think it means? To check this out,
we need Mathematica's linear algebra commands. Enter the augmented matrix
for our current problem as
A={{1,4,3,10},{2,1,-1,-1},{3,-1,-4,11}};
A // MatrixForm
This tells Mathematica to construct a matrix and fill
its entries from the following vectors of numbers, reading across
the first row, then the second, then the third. The "MatrixForm"
command tells Mathematica to print out A as a matrix rather
than as a list of vectors.
- First
let's see how to row reduce a step at a time. Then we will see
that a single command will do the whole job. Try the following
sequence of commands:
A1 = A;
A1 // MatrixForm
A1[[2]] = -2*A1[[1]] +
A1[[2]];
A1 // MatrixForm
A1[[3]] = -3*A1[[1]] +
A1[[3]];
A1 // MatrixForm
A1[[2]] = (-1/7)*A1[[2]];
A1 // MatrixForm
Got the idea? The double square brackets allow you to work
with one row of the matrix at a time. Finish the row reduction, or
at least take it far enough to decide what went wrong when you
asked Mathematica to solve the system of equations.
(The third type of row operation is swapping two rows. You may not
need it for this problem, but if you do, it works like this:
A2 = A;
A2 // MatrixForm
temp = A2[[2]];
A2[[2]] = A2[[3]];
A2[[3]]=temp;
A2 // MatrixForm
See if you can figure out what this does!)
- Finally,
let's go directly to the reduced row echelon form of in one
step:
RowReduce[A];
% // MatrixForm
This should show you in another way that our linear system is
inconsistent.
