Game Development Reference
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Adding any multiple of a row (column) to another row (column) does
not change the value of the determinant!
m
11
m
12
m
1n
m
11
m
12
m
1n
Adding one row to
another doesn't
change the
determinant
m
21
m
22
m
2n
m
21
m
22
m
2n
.
.
.
.
.
.
m
i1
m
i2
m
in
m
i1
+km
j1
m
i2
+km
j2
m
in
+km
jn
=
.
.
.
.
.
.
m
j1
m
j2
m
jn
m
j1
m
j2
m
jn
.
.
.
.
.
.
m
n1
m
n2
m
nn
m
n1
m
n2
m
nn
This explains why our shear matrices from Section 5.5 have a deter-
minant of 1.
6.1.4 Geometric Interpretation of Determinant
The determinant of a matrix has an interesting geometric interpretation. In
2D, the determinant is equal to the signed area of the parallelogram or skew
box that has the basis vectors as two sides (see Figure 6.1). (We discussed
Figure 6.1
The determinant
in 2D is the
signed area of
the skew box
formed by the
transformed
basis vectors.
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