Page 3 - Lesson Notes

 |adj A| = |A|
n-1
 adj (A ) = (adj A)
T
T
The area of a triangle whose vertices are (x 1, y 1), (x 2, y 2) and (x 3, y 3) is given by

NOTE: Since the area is a positive quantity we always take the absolute value
of the determinant.

Properties of Determinants
To find the value of the determinant, we try to make the maximum possible
zero in a row (or a column) by using properties given below and then expand
the determinant corresponding that row (or column).
Following are the various properties of determinants:
1. If all the elements of any row or column of a determinant are zero, then the
value of a determinant is zero.

2. If each element of any one row or one column of a determinant is a multiple
of scalar k, then the value of the determinant is a multiple of k. then the value
of the determinant is a multiple of k. i.e.

3. If in a determinant any two rows or columns are interchanged, then the
value of the determinant obtained is negative of the value of the given
determinant. If we make n such changes of rows (columns) indeterminant ∆
and obtain determinant ∆ , then ∆ 1 = (-1) ∆.
n

4. If all corresponding elements of any two rows or columns of a determinant
are identical or proportional, then the value of the determinant is zero.