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2.5.4 Method of Evaluating Determinant
i. Let us write two simultaneous equations as
a x + b y = m
1
1
a x + b y = n
2
2
Where x and y are the variables.
The common determinant ∆ is evaluated as
The determinant for x, i.e., ∆ is evaluated as
a
The determinant for y, i.e., ∆ is evaluated as
b
ii. If there are more than two simultaneous equations, say three, the method of evaluating the
determinants would be as illustrated below. Let the common determinant be
The procedure followed is like this. Select any row and the first column. Multiply each
element in the row or the column by its minor and by + sign or − sign and then add the
j+k
product. The multiplication by + sign or − sign is decided by a factor (−1) where the minor
of the element is appearing in row j and column k. Therefore, the determinant ∆ given above
is calculated as
= 5 (150 − 100) − 100(−21 + 6) + 10(− 350 + 150)
