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2
4
3
5
1 7 2
7 0 −3
2 −3 −1
(c)
This is an example of a symmetric matrix. A square matrix is sym-
metric if A T = A.
2
4
3
5
0
−4
3
4
0
−1
(d)
−3
1
0
This is an example of a skew symmetric or antisymmetric matrix. A
square matrix is skew symmetric if A T = −A. This implies that the
diagonal elements of a skew symmetric matrix must be 0.
6. Manipulate the following matrix expressions to remove the parentheses.
T
T
A T
(a)
T
BA T
CD T
(b)
T
(AB) T
D T C T
(c)
T
(AB) T (CDE) T
(d)
7. Describe the transformation aM = b represented by each of the following
matrices.
0 −1
1
(a) M =
0
2
2
2
2
(b) M =
2
2
2
2
2
0
(c) M =
0
2
4
0
(d) M =
0
7
−1
0
(e) M =
0
1
0 −2
2
(f) M =
0
8. For 3D row vectors a and b, construct a 3×3 matrix M such that a×b =
aM. That is, show that the cross product of a and b can be represented
as the matrix product aM, for some matrix M. (Hint: the matrix will be
skew-symmetric.)
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