Matrices

A^t means transpose the matrix. To do this, flip the columns and rows.

To add matrices, both matrices must be the same dimensions(rows by columns).

To multiply matrices, the dimensions of both matrices must match like so: (Matrix 1: A x B, Matrix 2: B x C. If both B's match, dimensions of resulting matrix will be A x C).

Multiplying matrices is too complicated to explain with words, so I'll just show you.

Ex 1.

A = [ 3 8 1 ] B = [ 2 0 9 ]

.......[ 4 0 -3 ] [ 4 -6 -5 ]

.......[ -2 1 5 ] [ 0 7 2 ]

Dimensions are 3 x 3.

Find A^t and B^t.

A^t = [ 3 4 -2] B^t = [ 2 4 0 ]

...........[ 8 0 1 ] [ 0 -6 7 ]

...........[ 1 -3 5 ] [ 9 -5 2 ]

Find A + B

A + B = [ 5 8 10]

..............[ 8 -6 -8 ]

..............[ -2 8 7 ]

^^^Everything you need for matrices.