> with(linalg);
Matrix Operations

> A := matrix([[2, 7, 1], [4, -5, 8]]);

> B := matrix([[3, 0, 4], [-2, 5, 1]]);

> C := matrix([[6, 5], [-2, 1], [3, 4]]);

> E := matrix(2, 2);

> A+B;
                                    A + B
> evalm(A+B);

> B[1, 2];
                                      0
> evalm(A+C);
Error, (in linalg:-matadd) matrix dimensions incompatible
> evalm(`.`(A, C));

Matrix Multiplication

> evalm(multiply(A, C));

> evalm(`.`(C, A));

> A1 := matrix([[1, 2], [2, 3], [0, 4], [-1, -2]]);

> B1 := matrix([[1, 2, 3], [4, 5, 6]]);

> evalm(`.`(A1, B1));

> multiply(A1, B1);

> evalm(`.`(B1, A1));
Error, (in linalg:-multiply) non matching dimensions for vector/matrix product
> A2 := matrix([[1, 2], [3, 4]]);

> B2 := matrix([[5, -1], [3, -2]]);

> evalm(`.`(A2, B2));

> evalm(`.`(B2, A2));

> evalm(2*B2);

The Identity Matrix

> array(1 .. 5, 1 .. 5, identity);

> diag(1, 1, 1, 1, 1);

> I2 := diag(1, 1);

> evalm(`.`(I2, B2));

> evalm(B2);

> evalm(`.`(B2, I2));

Transpose of a Matrix

> A := matrix([[2, 0, 3], [1, 4, 5]]);

> transpose(A);

Row Reduction and Linear Systems

One solution:

> M1 := matrix([[2, 1, -3, 0], [6, 3, -8, 0], [2, -1, 5, -4]]);

> rref(M1);

> gaussjord(M1);

> help("rref");
> M2 := matrix([[2, 6, -1, 8], [3, 9, 0, 15], [-2, -5, 6, 1]]);

> rref(M2);

No solutions (inconsistent):

> M3 := matrix([[1, 1, 1, 1], [4, 3, 5, 7], [2, 1, 3, 6]]);

> rref(M3);

Infinitely many solutions:

> M4 := matrix([[1, 2, -3, 1, 2], [3, 6, -8, -2, 1]]);

> rref(M4);

Elementary Matrices

> E := matrix([[0, 0, 1], [0, 1, 0], [1, 0, 0]]);

> A := matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);

> evalm(`.`(E, A));

> B := matrix([[-7, 5], [4, 1], [0, 26]]);

> evalm(`.`(E, B));

>