Matrices

Revise Matrices unit from G.C.E. (A/L) Combined Mathematics and G.C.E. (O/L) Mathematics.

Types of matrices

Zero matrix / Null matrix

All elements are .

Column matrix (column vector)

Only column.

Row matrix (row vector)

Only row.

Square matrix

Number of columns equal to number of rows.

Main diagonals of a square matrix

Formed by elements having equal subscripts.

Triangular matrix

Upper triangular matrix

All elements below the main diagonal are . Subset of square matrices.

Lower triangular matrix

All elements above the main diagonal are . Subset of square matrices.

Diagonal matrix

A square matrix whose with non-zero elements only on the main diagonal. Denoted by . Subset of upper and lower triangular matrices.

Identity matrix

Aka. unit matrix. A diagonal matrix and all diagonal elements are . Denoted by . Subset of diagonal matrices.

Matrix operations

Addition and subtraction

Order of the 2 matrices must be same. Matrix obtained by adding or subtracting corresponding elements.

Scalar multiplication

Matrix obtained by multiplying all elements by the scalar.