Let A be the matrix given in Exercise 34 . a) For each vector b that follows, determine whether b is in R ( A ) . b) If b is in R ( A ) , then exhibit a vector x in R 3 such that A x = b . c) If b is in R ( A ) , then write b as a linear combination of the columns of A . i) b = [ 1 2 0 ] ii) b = [ 1 1 − 1 ] iii) b = [ 4 7 2 ] iv) b = [ 0 1 2 ] v) b = [ 0 1 − 2 ] vi) b = [ 0 0 0 ] 34. A = [ 1 − 2 1 2 − 3 5 1 0 7 ]
Let A be the matrix given in Exercise 34 . a) For each vector b that follows, determine whether b is in R ( A ) . b) If b is in R ( A ) , then exhibit a vector x in R 3 such that A x = b . c) If b is in R ( A ) , then write b as a linear combination of the columns of A . i) b = [ 1 2 0 ] ii) b = [ 1 1 − 1 ] iii) b = [ 4 7 2 ] iv) b = [ 0 1 2 ] v) b = [ 0 1 − 2 ] vi) b = [ 0 0 0 ] 34. A = [ 1 − 2 1 2 − 3 5 1 0 7 ]
Solution Summary: The author explains that the vector b is left[cc1& -2& 1 2&
a) For each vector
b
that follows, determine whether
b
is in
R
(
A
)
.
b) If
b
is in
R
(
A
)
, then exhibit a vector
x
in
R
3
such that
A
x
=
b
.
c) If
b
is in
R
(
A
)
, then write
b
as a linear combination of the columns of
A
.
i)
b
=
[
1
2
0
]
ii)
b
=
[
1
1
−
1
]
iii)
b
=
[
4
7
2
]
iv)
b
=
[
0
1
2
]
v)
b
=
[
0
1
−
2
]
vi)
b
=
[
0
0
0
]
34.
A
=
[
1
−
2
1
2
−
3
5
1
0
7
]
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.
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