Basic Matrix Operations

A is a 2 × 2 matrix, with entries:

Compute:

The column vectors of A are:

The transpose of A is

The products AB and BA are not equal:

A times a vector gives a linear combination of the columns of A:

Multiplying by the identity leaves a matrix un changed :

The inverse of A is

Check:

To compute the de terminant of the 3 × 3 matrix

we first find the three submatrices

and then use the co factor expansion across the first row:

det(C) = 2 det(C₁₁) - 4 det(C₁₂) + (-1) det(C₁₃) =