>> A = [1 -3 2; -2 4 1] **** input A A = 1 -3 2 -2 4 1 >> B = [0 1; -3 4; -1 2], C = rand(3,3) B = 0 1 -3 4 -1 2 C = 0.9501 0.4860 0.4565 0.2311 0.8913 0.0185 0.6068 0.7621 0.8214 >> bb = [1;2] *** will solve A*x = bb bb = 1 2 >> A(:,1) **** pick the first column of A ans = 1 -2 >> A*B, B*A **** A*B may not equal B*A ans = 7 -7 -13 16 ans = -2 4 1 -11 25 -2 -5 11 0 >> eye(3) **** generate identity matrix ans = 1 0 0 0 1 0 0 0 1 >> inv(C) ans = 1.6740 -0.1196 -0.9276 -0.4165 1.1738 0.2050 -0.8504 -1.0006 1.7125 >> inv(C)*C ans = 1.0000 0.0000 0 0.0000 1.0000 0 0 -0.0000 1.0000 >> rref(A) ans = 1.0000 0 -5.5000 0 1.0000 -2.5000 >> x = A\bb x = 0 0.2727 0.9091 >> rref([A bb]) ans = 1.0000 0 -5.5000 -5.0000 0 1.0000 -2.5000 -2.0000