• $\begin{array}{l}y=\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right]\times 6\\ \mathrm{>>>}y=\left[\begin{array}{ccc}6& 0& 0\\ 0& 12& 0\\ 0& 0& 18\end{array}\right]\end{array}$

• $\begin{array}{l}m=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]\\ \det \left(m\right)\\ \mathrm{>>>}0\end{array}$

• $\begin{array}{l}A=\left[\begin{array}{cc}1& 2\\ 3& 5\end{array}\right]\\ R\left(A\right)\\ \mathrm{>>>}2\end{array}$

• $\begin{array}{l}m=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 18& 9\end{array}\right]\\ m^{\mathrm{T}}\\ \mathrm{>>>}\left[\begin{array}{ccc}1& 4& 7\\ 2& 5& 18\\ 3& 6& 9\end{array}\right]\end{array}$

• $\begin{array}{l}m=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 18& 9\end{array}\right]\\ m^{\mathrm{*}}\\ \mathrm{>>>}\left[\begin{array}{ccc}-63& 36& -3\\ 6& -12& 6\\ 37& -4& -3\end{array}\right]\end{array}$

• $\begin{array}{l}m=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 18& 9\end{array}\right]\\ m^{-1}\\ \mathrm{>>>}\left[\begin{array}{ccc}-1.05& 0.6& -0.05\\ 0.1& -0.2& 0.1\\ 0.616666666666667& -0.0666666666666667& -0.05\end{array}\right]\end{array}$

• $\begin{array}{l}A=\left[\begin{array}{cccc}3& -2& 4& -2\\ 5& 3& -3& -2\\ 5& -2& 2& -2\\ 5& -2& -3& 3\end{array}\right]\\ \mathrm{EigVal}\left(A\right)\\ \mathrm{>>>}\{-2:1,3:1,5:2\}\end{array}$

Matrix A has eigenvalues -2, 3, and 5, and that the eigenvalues -2 and 3 have algebraic multiplicity 1 and that the eigenvalue 5 has algebraic multiplicity 2.

• $\begin{array}{l}A=\left[\begin{array}{cccc}3& -2& 4& -2\\ 5& 3& -3& -2\\ 5& -2& 2& -2\\ 5& -2& -3& 3\end{array}\right]\\ \mathrm{EigVec}\left(A\right)\\ \mathrm{>>>}\left[\begin{array}{c}(-2,1,\left[\left[\begin{array}{c}0\\ 1\\ 1\\ 1\end{array}\right]\right]),(3,1,\left[\left[\begin{array}{c}1\\ 1\\ 1\\ 1\end{array}\right]\right]),(5,2,\left[\begin{array}{c}\left[\begin{array}{c}1\\ 1\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ -1\\ 0\\ 1\end{array}\right]\end{array}\right])\end{array}\right]\end{array}$

• $\begin{array}{l}\mathrm{v1}=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]\\ \mathrm{v2}=\left[\begin{array}{ccc}4& 5& 6\end{array}\right]\\ \mathrm{dot}(\mathrm{v1},\mathrm{v2})\\ \mathrm{>>>}32\end{array}$

• $\begin{array}{l}\mathrm{v1}=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]\\ \mathrm{v2}=\left[\begin{array}{ccc}4& 5& 6\end{array}\right]\\ \mathrm{cross}(\mathrm{v1},\mathrm{v2})\\ \mathrm{>>>}\left[\begin{array}{ccc}-3& 6& -3\end{array}\right]\end{array}$

• $\begin{array}{l}A=\left[\begin{array}{cc}4& 3\\ 1.5& 1\end{array}\right]\\ L,U=\mathrm{LU}\left(A\right)\\ \mathrm{>>>}L=\left[\begin{array}{cc}1& 0\\ 0.375& 1\end{array}\right]\\ \mathrm{>>>}U=\left[\begin{array}{cc}4& 3\\ 0& -0.125\end{array}\right]\end{array}$

• $\begin{array}{l}A=\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 3\\ 2& 3& 4\end{array}\right]\\ Q,R=\mathrm{QR}\left(A\right)\\ \mathrm{>>>}Q=\left[\begin{array}{ccc}0.408248290463863& -0.577350269189626& -0.707106781186548\\ 0.408248290463863& -0.577350269189626& 0.707106781186548\\ 0.816496580927726& 0.577350269189626& 0\end{array}\right]\\ \mathrm{>>>}R=\left[\begin{array}{ccc}2.44948974278318& 3.2659863237109& 4.89897948556636\\ 0& 0.577350269189626& 0\\ 0& 0& 1.4142135623731\end{array}\right]\end{array}$

• $\begin{array}{l}A=\left[\begin{array}{ccc}1& 2& 0\\ 0& 3& 0\\ 2& -4& 2\end{array}\right]\\ P,D=\mathrm{Diag}\left(A\right)\\ \mathrm{>>>}P=\left[\begin{array}{ccc}-1& 0& -1\\ 0& 0& -1\\ 2& 1& 2\end{array}\right]\\ \mathrm{>>>}D=\left[\begin{array}{ccc}1& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right]\end{array}$