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Chapter 2
Euclidean Space 2.1 Practice Problems [
]
−4
1. u − w = [
[
3 4
−
−1
]
]
[
0 =
−2
[
6
v + 3w =
5
] 5 0 =
+3 [
−2w + u + 3v = −2
5 0 −2
]
]
[
3− 0 4 − (−2)
=
3 6
[
−1 + 3 (5)
−9
]
]
[
6 + 3 (0) = [
+
−4 − 5
−4
]
[
3
−1
]
6 2
+3 4
]
14 6
[ =
]
−2 (5) + (−4) + 3 (−1) −2 (0) + 3 + 3 (6) = −2 (−2) + 4 + 3 (2)
2. (a) −x1 + 4x2 = 3 7x1 + 6x2 = 10 2x1 − 6x2 = 5
− x3 = 4 − 2x2 + 2x3 = 7 − 5x2 + 9x3 = 11 + 6x2 + 5x3 = −6
(b) 3x1 4x1 2x1 [ 3. (a) x1
[ (b) x1
[ 4. (a)
x1 x2
]
1 −5 4 4 0 3
[
+ x2
]
[ + x2
x3
1 7 0
−3 2 12
]
[
+ x3
−2
]
6
=
−8 ]
[ + x3
−1 5 6
[
]
3 12 0 [
+ x4
]
] 5 −2 = 0
[
0 6 10
]
]
[ =
5 7
]
[
−17 21 14
]