NULL; restart; NULL; with(linalg); A := matrix([[-1, 2, 3], [4, -5, 6], [7, 8, -9]]); B := matrix([[0, 1, 2], [1, 2, 2], [2, 1, 0]]); A*B; multiply(A, B); evalm(`&*`(A, B)); NULL; NULL; C := evalm(A+B); evalm(C^2); multiply(C, C); evalm(A^2+B^2)+2*multiply(A, B); evalm(2*multiply(A, B)); evalm(evalm(A^2+B^2)+2*multiply(A, B)); w := vector([1, 3, 4]); NULL; NULL; Aw := augment(A, w); reducedMatrix := rref(Aw); X := col(reducedMatrix, 4); X := linsolve(A, w); X := multiply(inverse(A), w); det(A); NULL; A := matrix([[1, 1, 1, 2, 6], [2, 3, -2, 1, -3], [3, 5, -5, 1, -8], [4, 3, 8, 2, 3]]); NULL; rref(A); colspace(A); rowspace(A); nullspace(A); linsolve(A, vector([0, 0, 0, 0])); At := transpose(A); colspace(At); NULL; P := matrix([[1, 2, 3], [2, -1, 1], [3, 0, 0]]); lambda := -3; linsolve(evalm(P-lambda*diag(1, 1, 1)), vector([0, 0, 0])); NULL; v1 := vector([-2, 1, 2]); ; NULL; A := augment(v1, vector([1, 1, 1]), vector([2, 2, 2])); NULL; rank(A); rref(A); coldim(A); NULL; rowdim(A);