Let H=Span{v1,v2} and
K=Span{v3,v4}, where
v1,v2,v3,v4 are given
below.
v1 = [3 2 5], v2 =[4...
Let H=Span{v1,v2} and
K=Span{v3,v4}, where
v1,v2,v3,v4 are given
below.
v1 = [3 2 5], v2 =[4 2 6], v3
=[5 -1 1], v4 =[0 -21 -9]
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 vector w that
generates that line.
w = { _______ }
S = {<3, -2, 1, -4>, <2, 1, -2, -2>, <0, -7, 8,
-2>}
Determine whether...
S = {<3, -2, 1, -4>, <2, 1, -2, -2>, <0, -7, 8,
-2>}
Determine whether b = < -4, 12, -12, 8 >
is in the span of S. Please write out the vector equation by
definition of span. Then convert the vector equation into system of
linear equations and matrix equation. No need to solve the
equation.
The projection of the vector (1,1,-1) onto the subspace
span{(1,-1,1), (1,1,0)} is given by:
a)(1,-1,0)
b)(1,1,0)...
The projection of the vector (1,1,-1) onto the subspace
span{(1,-1,1), (1,1,0)} is given by:
a)(1,-1,0)
b)(1,1,0)
c) (-1/3, 1)
d)(2, 4, -1)
e)(2/3, 4/3, -1/3)
f)None of the above
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.
Suppose the vectors v1, v2, . . . , vp span a vector space V
....
Suppose the vectors v1, v2, . . . , vp span a vector space V
.
(1) Show that for each i = 1, . . . , p, vi belongs to V ;
(2) Show that given any vector u ∈ V , v1, v2, . . . , vp, u also
span V