The Determinant

The definition of the determinant of a matrix is something we will not need in this course. What we will need is to use the determinant. Here are some examples of computations.

In[73]:=

  a={{a11, a12},{a21, a22}}

Out[73]=

  {{a11, a12}, {a21, a22}}

In[74]:=

  Det[a]

Out[74]=

  -(a12 a21) + a11 a22

In[75]:=

  b={{b11, b12, b13},{b21, b22, b23},{b31, b32, b33}}

Out[75]=

  {{b11, b12, b13}, {b21, b22, b23}, {b31, b32, b33}}

In[76]:=

  Det[b]

Out[76]=

  -(b13 b22 b31) + b12 b23 b31 + b13 b21 b32 - b11 b23 b32 - 
   
    b12 b21 b33 + b11 b22 b33

In[77]:=

  c={{2, 1, 0, 1},{3, 2, 1, 2},{4, 0, 1, 4},{1, 0, 2, 1}}

Out[77]=

  {{2, 1, 0, 1}, {3, 2, 1, 2}, {4, 0, 1, 4}, {1, 0, 2, 1}}

In[78]:=

  Det[c]

Out[78]=

-7

Up to Two Important Functions of a Matrix