[M] Let H = Span { v 1 , v 2 } and K = Span { v 3 , v 4 }, where v 1 = [ 5 3 8 ] , v 2 = [ 1 3 4 ] , v 3 = [ 2 − 1 5 ] , v 4 = [ 0 − 12 − 28 ] Then H and K are subspaces of ℝ 3 . In fact, H and K are planes in ℝ 3 through the origin, and they intersect in a line through 0 . Find a nonzero vector w that generates that line. [ Hint: w can be written as c 1 v 1 + c 2 v 2 and also as c 3 v 3 + c 4 v 4 . To build w , solve the equation c 1 v 1 + c 2 v 2 = c 3 v 3 + c 4 v 4 for the unknown c j ’s.]
[M] Let H = Span { v 1 , v 2 } and K = Span { v 3 , v 4 }, where v 1 = [ 5 3 8 ] , v 2 = [ 1 3 4 ] , v 3 = [ 2 − 1 5 ] , v 4 = [ 0 − 12 − 28 ] Then H and K are subspaces of ℝ 3 . In fact, H and K are planes in ℝ 3 through the origin, and they intersect in a line through 0 . Find a nonzero vector w that generates that line. [ Hint: w can be written as c 1 v 1 + c 2 v 2 and also as c 3 v 3 + c 4 v 4 . To build w , solve the equation c 1 v 1 + c 2 v 2 = c 3 v 3 + c 4 v 4 for the unknown c j ’s.]
Solution Summary: The author explains the nonzero vector w that generates the line through zero.
[M] Let H = Span {v1, v2} and K = Span {v3, v4}, where
v
1
=
[
5
3
8
]
,
v
2
=
[
1
3
4
]
,
v
3
=
[
2
−
1
5
]
,
v
4
=
[
0
−
12
−
28
]
Then H and K are subspaces of ℝ3. In fact, H and K are planes in ℝ3 through the origin, and they intersect in a line through 0. Find a nonzero vectorw that generates that line. [Hint:w can be written as c1v1 + c2v2 and also as c3v3 + c4v4. To build w, solve the equation c1v1 + c2v2 = c3v3 + c4v4 for the unknown cj’s.]
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.
Elementary Algebra For College Students (9th Edition)
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