8. Vector and matrix

aa = {a1, a2, a3}  ; bb={b1, b2, 
        b3}

aa + bb

aa bb

aa . bb

mm = {{m1, m2, m3}, {m4, m5, m6}}
MatrixForm[mm]

e33 = 4 IdentityMatrix[3]

mm . 
        e33//MatrixForm

mm . aa

Print[aa[[1]], " ", mm[[2]], " ", 
      mm[[1, 3]]]

Print["row=", Length[mm], " column=", 
      Length[mm[[1]]]]

<< LinearAlgebra`MatrixManipulation`

TakeMatrix[mm, {1, 1}, {2, 2}] // MatrixForm

BlockMatrix[{{mm, ZeroMatrix[2]}, {e33, Transpose[mm]}}] // 
      MatrixForm

maa = {{5, -4}, {-4, 5}}
vbb = {-3, 6}

LinearSolve[maa, vbb]