Page 38 - Standard Handbook Of Petroleum & Natural Gas Engineering

Trigonometry 27

3. If two columns are equal or if one is a multiple of the other, the deter-
minant is zero.
4. To multiply a determinant by any number m, multiply all elements of any
one column by m.
Systems of simultaneous equations may be solved by the use of determinants
in the following manner. Although the example is a third-order system, larger
systems may be solved by this method. If
a,x + b,y + c,z = p,
a,x + b,y + c?z = p2

agx + b,y + clz = p1
and if

then
x = D,/D

y = D,/D
z = DJD

where

TRIGONOMETRY
Directed Angles

If AB and AB' are same end point A, the directed
<BAB' is the ordered is the initial side of <BAB' and A
the terminal side. <BAB' # <B'AB and any directed angle may be I 0" or 2 180".