Properties of Determinants
- The value of a determinant remains unchanged if rows are changed to columns and to columns to rows.
- If two rows (or two columns) are interchanged, the sign of the determinant is changed.
- If two rows (or two columns) are identical, the value of the determinant is zero.
- If the elements of any rows (or column) are multiplied a common factor, the determinant is multiplied by that factor.
- If the elements of any rows (or column) are increased (or decreased) by equal multiples of the corresponding elements of any other row (or column), the value of the determinant is unchanged.
Matrices
- Definition
An m × n
matrix A is a rectangular array of elements (numbers or functions) with m
rows and n columns.
- Square matrix is a matrix of order n × n
- A square matrix ⌊ aij ⌋ is symmetric if aij = aij , i.e. it is symmetric about the leading diagonal.
- A square matrix ⌊ aij ⌋ is skew-symmetric if aij = – aij .
- Diagonal matrix is a square matrix with all elemets zero except those on the leading diagonal.
- Unit matrix is a diagonal matrix in which the elements on the leadigonal are all unity. The unit matrix is denoted by I.
- A null matrix is one whose elements are al zero.
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