Let A = [ 1 0 − 4 0 3 − 2 − 2 6 3 ] and b = [ 4 1 − 4 ] . Denote the columns of A by a 1 , a 2 , a 3 , and let W = Span{ a 1 , a 2 , a 3 }. a. Is b in { a 1 , a 2 , a 3 }? How many vectors are in { a 1 , a 2 , a 3 }? b. Is b in W ? How many vectors are in W ? c. Show that a 1 is in W . [ Hint: Row operations are unnecessary.]
Let A = [ 1 0 − 4 0 3 − 2 − 2 6 3 ] and b = [ 4 1 − 4 ] . Denote the columns of A by a 1 , a 2 , a 3 , and let W = Span{ a 1 , a 2 , a 3 }. a. Is b in { a 1 , a 2 , a 3 }? How many vectors are in { a 1 , a 2 , a 3 }? b. Is b in W ? How many vectors are in W ? c. Show that a 1 is in W . [ Hint: Row operations are unnecessary.]
Let A =
[
1
0
−
4
0
3
−
2
−
2
6
3
]
and b =
[
4
1
−
4
]
. Denote the columns of A by a1, a2, a3, and let W = Span{a1, a2, a3}.
a. Is b in {a1, a2, a3}? How many vectors are in {a1, a2, a3}?
b. Is b in W? How many vectors are in W?
c. Show that a1 is in W. [Hint: Row operations are unnecessary.]
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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