Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Also notice how matrices print. All columns have the same width and entries in a given column are right justified.
Next we compute the reduced row echelon form of A.
sage: A.rref()
[ 1 0 -1933/3]
[ 0 1 1550/3]
3.1 Indexing
Sage has quite flexible ways of extracting elements or submatrices from a matrix:
sage: m=[(1, -2, -1, -1,9), (1, 8, 6, 2,2), (1, 1, -1, 1,4), (-1, 2, -2, -1,4)];M= matrix(m)
sage: M
[ 1 -2 -1 -1 9]
[ 1 8 6 2 2]
[ 1 1 -1 1 4]
[-1 2 -2 -1 4]
Get the 2 x 2 submatrix of M, starting at row index and column index 1:
sage: M[1:3,1:3]
[ 8 6]
[ 1 -1]
Get the 2 x 3 submatrix of M starting at row index and column index 1:
sage: M[1:3,[1..3]]
[ 8 6 2]
[ 1 -1 1]
Get the second column of M:
sage: M[:,1]
[-2]
[ 8]
[ 1]
[ 2]
Get the first row of M:
sage: M[0,:]
[ 1 -2 -1 -1 9]
Get the last row of M (negative numbers count from the end):
sage: M[-1,:]
[-1 2 -2 -1 4]
More examples:
sage: M[range(2),:]
[ 1 -2 -1 -1 9]
[ 1 8 6 2 2]
sage: M[range(2),4]
[9]
[2]
sage: M[range(3),range(5)]
[ 1 -2 -1 -1 9]
[ 1 8 6 2 2]
60 Chapter 3. Matrices over an arbitrary ring