The word
‘determinant’ comes from the word ‘determine’. What do we determine
using a determinant? The answer is ‘solutions’. Determinants are used mainly to
find the solutions of systems of linear equations. The study of determinants began only in
the sixteenth-seventeenth centuries. Some of the mathematicians who contributed to this
branch of Algebra are Hamilton, Jacobi, Cayley, Sylvester, Cramer and others.
To understand what a determinant is, let us take the pair of equations, ax + by = p
cx + dy = q
In any system of equations like this, the values of a, b, c, d, p, q determine the values
of x and y.These numbers are called the coefficients. When this system is solved, we get the
solution as,
x = (pd – qb)/(ad – bc)
y = (aq – cp)/(ad – bc).
Here, the denominators are the same. This number namely,
ad – bc is
called the determinant of a, b, c, and d of 2nd order, written as a b c d
and d of 2nd order, written as
In the same way, a system of 3 linear equations leads to a determinant of 3rd
order. The determinant of the system, a1x + b1y + c1z = d1
whose value is a1(b2c3 – b3c2)
+ b1(c2a3 – c3a2) + c1(a2b3
– a3b2). |
