[M] Let a 1 ,…,a 5 denote the columns of the matrix A , where A = [ 5 1 2 2 0 3 3 2 − 1 − 12 8 4 4 − 5 12 2 1 1 0 − 2 ] , B = [ a 1 a 2 a 3 ] Explain why a 3 and a 5 are in the column space of B . Find a set of vectors that spans Nul A . Let T : ℝ 5 → ℝ 4 be defined by T ( x ) = A x . Explain why T is neither one-to-one nor onto.
[M] Let a 1 ,…,a 5 denote the columns of the matrix A , where A = [ 5 1 2 2 0 3 3 2 − 1 − 12 8 4 4 − 5 12 2 1 1 0 − 2 ] , B = [ a 1 a 2 a 3 ] Explain why a 3 and a 5 are in the column space of B . Find a set of vectors that spans Nul A . Let T : ℝ 5 → ℝ 4 be defined by T ( x ) = A x . Explain why T is neither one-to-one nor onto.
[M] Let a1,…,a5 denote the columns of the matrix A, where
A
=
[
5
1
2
2
0
3
3
2
−
1
−
12
8
4
4
−
5
12
2
1
1
0
−
2
]
,
B
=
[
a
1
a
2
a
3
]
Explain why a3 and a5 are in the column space of B.
Find a set of vectors that spans Nul A.
Let T : ℝ5 → ℝ4 be defined by T(x) = Ax. Explain why T is neither one-to-one nor onto.
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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