In Exercises 5-8, find the coordinate vector [ x ] B of x relative to the given basis B = { b 1 ,..., b n }. 7. b 1 = [ 1 − 1 − 3 ] , b 2 = [ − 3 4 9 ] , b 3 = [ 2 − 2 4 ] , x = [ 8 − 9 6 ]
In Exercises 5-8, find the coordinate vector [ x ] B of x relative to the given basis B = { b 1 ,..., b n }. 7. b 1 = [ 1 − 1 − 3 ] , b 2 = [ − 3 4 9 ] , b 3 = [ 2 − 2 4 ] , x = [ 8 − 9 6 ]
In Exercises 5-8, find the coordinate vector [ x ]B of x relative to the given basis B = {b1,...,bn}.
7.
b
1
=
[
1
−
1
−
3
]
,
b
2
=
[
−
3
4
9
]
,
b
3
=
[
2
−
2
4
]
,
x
=
[
8
−
9
6
]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Let B = {b₁,b₂} be the basis in R2 pictured below.
a=
b=
f the coordinate vectors [u]}8 = []
C =
d=
b₂
(enter integers)
0
91
and VB
[[3]
find a, b, c, and d.
In Exercises 5-8, find the coordinate vector [x] of x relative to the given
basis B = {b₁,..., bn}.
5.
b₁ =
[3],
-3
, b₂
=
2
[3]
-5
"
X =
[
-2
1
Linear Algebra. Please write your answer clearly. Thanks.
Chapter 4 Solutions
Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e
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