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 = { _______ }
If S=(v1,v2,v3,v4)
is a linearly independent sequence of vectors in Rn
then
A) n = 4...
If S=(v1,v2,v3,v4)
is a linearly independent sequence of vectors in Rn
then
A) n = 4
B) The matrix ( v1 v2 v3
v4) has a unique pivot column.
C) S is a basis for
Span(v1,v2,v3,v4)
. Let v1,v2,v3,v4 be a basis of V. Show that v1+v2, v2+v3,
v3+v4, v4 is a...
. Let v1,v2,v3,v4 be a basis of V. Show that v1+v2, v2+v3,
v3+v4, v4 is a basis of V
If S is the set of vectors in R^4 (S= {v1, v2, v3, v4, v5})
where,...
If S is the set of vectors in R^4 (S= {v1, v2, v3, v4, v5})
where, v1 = (1,2,-1,1), v2 = (-3,0,-4,3), v3 = (2,1,1,-1), v4 =
(-3,3,-9,-6), v5 = (3,9,7,-6)
Find a subset of S that is a basis for the span(S).
Let v1=(0,1,2,3),v2=(1,0,-1,0),v3=(0,4,-1,2), and v4=(0,5,1,5).
Let S=(v1,v2,v3,v4)
(1)find a basis for span(S)
(2)is the vector e1=(1,0,0,0) in...
Let v1=(0,1,2,3),v2=(1,0,-1,0),v3=(0,4,-1,2), and v4=(0,5,1,5).
Let S=(v1,v2,v3,v4)
(1)find a basis for span(S)
(2)is the vector e1=(1,0,0,0) in the span of S? Why?
Determine all real numbers a for which the vectors
v1 = (1,−1,1,a,2)
v2 = (−1,0,0,1,0)
v3...
Determine all real numbers a for which the vectors
v1 = (1,−1,1,a,2)
v2 = (−1,0,0,1,0)
v3 = (1,2,a + 1,1,0)
v4 = (2,0,a + 3,2a + 3,4)
make a linearly independent set. For which values of a does the
set contain at least three linearly independent vectors?
Let S =
{v1,v2,v3,v4,v5}
where v1= (1,−1,2,4), v2 = (0,3,1,2),
v3 = (3,0,7,14), v4 = (1,−1,2,0),...
Let S =
{v1,v2,v3,v4,v5}
where v1= (1,−1,2,4), v2 = (0,3,1,2),
v3 = (3,0,7,14), v4 = (1,−1,2,0),
v5 = (2,1,5,6). Find a subset of S that forms a basis
for span(S).
Using MATLAB solve:
The vectors v1=(1,-1,1), v2=(0,1,2), v3=(3,0,1) span R3. Express
w=(x,y,z) as linear combination of...
Using MATLAB solve:
The vectors v1=(1,-1,1), v2=(0,1,2), v3=(3,0,1) span R3. Express
w=(x,y,z) as linear combination of v1,v2,v3.
1. Prove that if {⃗v1, ⃗v2, ⃗v3} is a linear dependent set of
vectors in V...
1. Prove that if {⃗v1, ⃗v2, ⃗v3} is a linear dependent set of
vectors in V , and if ⃗v4 ∈ V , then {⃗v1, ⃗v2, ⃗v3, ⃗v4} is
also a linear dependent set of vectors in V .
2. Prove that if {⃗v1,⃗v2,...,⃗vr} is a linear dependent set of
vectors in V, and if⃗ vr + 1 ,⃗vr+2,...,⃗vn ∈V, then
{⃗v1,⃗v2,...,⃗vn} is also a linear dependent set of vectors in
V.
Verify that the following vectors form an orthogonal list:
v1=1, 1, 2 v2= 2,0,-1] v3=1,...
Verify that the following vectors form an orthogonal list:
v1=1, 1, 2 v2= 2,0,-1] v3=1, −5, 2