Transposing a Matrix

Reduced-Row Echelon Form

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 x – 2y + 3z = 14 2x + y – z = – 3

4x – 2y + 2z = 14

can be written as the augmented matrix

1 –2 3 14

21 –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

15-14

Matrices