Game Development Reference
In-Depth Information
3.
AB = (4×3)(3×3) = 4×3
AH = (4×3)(3×1) = 4×1
BB = (3×3)(3×3) = 3×3
BH = (3×3)(3×1) = 3×1
CC = (2×2)(2×2) = 2×2
DC = (5×2)(2×2) = 5×2
EB = (1×3)(3×3) = 1×3
EH = (1×3)(3×1) = 1×1
FE = (4×1)(1×3) = 4×3
FG = (4×1)(1×4) = 4×4
GA = (1×4)(4×3) = 1×3
GF = (1×4)(4×1) = 1×1
HE = (3×1)(1×3) = 3×3
HG = (3×1)(1×4) = 3×4
(1)(−3)+(−2)(4)
1 −2
5
−3
7
(1)(7)+(−2)(1/3)
4.
(a)
=
0
4
1/3
(5)(−3)+(0)(4)
(5)(7)+(0)(1/3)
−3+(−8)
7+(−2/3)
−11
19/3
=
=
−15+0
35+0
−15
35
(b) Not possible; cannot multiply a 2 × 2 matrix by a 1 × 2 vector on the right.
2
4
−2
3
5
0
3
(c)
3 −1
4
5
7
−6
1
−4
2
=
(3)(−2)+(−1)(5)+(4)(1)
(3)(0)+(−1)(7)+(4)(−4)
(3)(3)+(−1)(−6)+(4)(2)
=
−6+(−5)+4
0+(−7)+(−16)
9+6+8
=
−7 −23
23
2
4
1
3
5
0
0
0
0
1
0
0
(d)
x
y
z
w
=
x
y
z
w
0
0
1
0
0
0
0
1
(e) Not possible; cannot multiply a 1×4 vector by a 2×1 vector.
m
11
1
0
m
11
m
12
m
12
(f)
=
0
1
m
21
m
22
m
21
m
22
6
−7
(g)
3
3
=
(3)(6) + (3)(−4)
(3)(−7) + (3)(5)
−4
5
=
18 + (−12) −21 + 15
=
6 −6
(h) Not possible; cannot multiply a 3×3 matrix by a 2×3 matrix on the right.
2
4
3
5
1
0
0
5.
(a)
5 −1
2
0
1
0
0
0
1
=
(5)(1)+(−1)(0)+(2)(0)
(5)(0)+(−1)(1)+(2)(0)
(5)(0)+(−1)(0)+(2)(1)
=
5 −1
2
2
4
3
5
2
4
3
5
2
4
3
5
2
4
3
5
1
0
0
−1
2
(1)(5) + (0)(−1) + (0)(2)
(0)(5) + (1)(−1) + (0)(2)
(0)(5) + (0)(−1) + (1)(2)
−1
2
0
1
0
=
=
0
0
1
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