August 2014
Intermediate to advanced
469 pages
16h 30m
English
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Linear and Affine Algebra 287
FIGURE 6.3: A visualization of the expansion by rows zero and one of a
4 × 4 matrix in order to compute the determinant.
To compute the inverse of a 4 × 4matrixA, first construct the adjoint
matrix. The cofactors involve 3 × 3 determinants. For example, the entry in
row zero and column zero of adjoint(A)is
+det
⎡
⎣
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
⎤
⎦
=+a
11
· det
a
22
a
23
a
32
a
33
− a
12
· det
a
21
a
23
a
31
a
33
+ a
13
· det
a
21
a
22
a
31
a
32
(6.46)
This equation involves determinants of 2 × 2 submatrices that also occur in
the equation for the determinant of the 4×4 matrix. This suggests computing
all of the entries of adjoint(A) using only 2 × 2 submatr ...