HP 39gs User Manual page 202

Transposing a
Matrix
Reduced-Row
Echelon Form
15-14
The TRN function swaps the row-column and column-row
elements of a matrix. For instance, element 1,2 (row 1,
column 2) is swapped with element 2,1; element 2,3 is
swapped with element 3,2; and so on.
For example, TRN([[1,2],[3,4]]) creates the matrix
[[1,3],[2,4]].
The following set of equations
can be written as the augmented matrix
1 2 – 3 14
2 1 1 – 3 –
4 2 – 2 14
which can then stored as a
×
3 4
real matrix in any
matrix variable. M1 is used
in this example.
You can use the RREF
function to change this to
reduced row echelon form,
storing it in any matrix
variable. M2 is used in this
example.
The reduced row echelon
matrix gives the solution to
the linear equation in the
fourth column.
An advantage of using the
RREF function is that it will also work with inconsistent
matrices resulting from systems of equations which have
no solution or infinite solutions.
For example, the following set of equations has an infinite
number of solutions:
x + y z – = 5
2x y – = 7
x 2y – + z = 2
x 2y – + 3z = 14
2x + y z – = – 3
4x – 2y + 2z = 14
Matrices