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 $0$. $$

Column matrix (column vector)

Only $1$ column. $$

Row matrix (row vector)

Only $1$ 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 $0$. Subset of square matrices. $$

Lower triangular matrix

All elements above the main diagonal are $0$. Subset of square matrices. $$

Diagonal matrix

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

Identity matrix

Aka. unit matrix. A diagonal matrix and all diagonal elements are $1$. Denoted by $I$. 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.