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?
5. Let v1 = (1/3,−2/3,2/3), v2 = (2/3,−1/3,−2/3) and v3 =
(2/3,2/3,1/3).
(a) Verify that v1,...
5. Let v1 = (1/3,−2/3,2/3), v2 = (2/3,−1/3,−2/3) and v3 =
(2/3,2/3,1/3).
(a) Verify that v1, v2, v3 is an orthonormal basis of R 3 .
(b) Determine the coordinates of x = (9, 10, 11), v1 − 4v2 and
v3 with respect to v1, v2, v3.
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).
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.
Let S = {v1, v2, v3, v4} be a given basis of R ^4 . Suppose...
Let S = {v1, v2, v3, v4} be a given basis of R ^4 . Suppose that
A is a (3 × 4) matrix with the following properties: Av1 = 0, A(v1
+ 2v4) = 0, Av2 =[ 1 1 1 ] T , Av3 = [ 0 −1 −4
]T . Find a basis for N (A), and a basis for R(A). Fully
justify your answer.
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1
and v2 with the same...
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1
and v2 with the same span as x1, x2. Now use the formula
p =((y, v1)/(v1, v1))v1 + ((y, v2)/(v2, v2))v2
to compute the projection of y onto that span. Of course,
replace the inner product with the dot product when working with
standard vectors
1)
Compute the projection of y = (1, 2, 3) onto span
(x1, x2) where
x1 =(1, 1, 1) x2 =(1, 0, 1)
The inner...
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).
Use Gram-Schmidt process to transform the basis {u1, u2, u3},
where u1=(1,1,1), u2=(1,2,0), u3=(1,0,-1),:
a) for...
Use Gram-Schmidt process to transform the basis {u1, u2, u3},
where u1=(1,1,1), u2=(1,2,0), u3=(1,0,-1),:
a) for the Euclidean IPS. (IPS means inner product space)
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1
and v2 with the same...
first use Gram-Schmidt on x1, x2 to create orthogonal vectors v1
and v2 with the same span as x1, x2. Now use the formula
p =((y, v1)/(v1, v1))v1 + ((y, v2)/(v2, v2))v2
to compute the projection of y onto that span. Of course,
replace the inner product with the dot product when working with
standard vectors
2)
Compute the projection of y = (1, 2, 2, 2, 1) onto
span (x1, x2) where
x1 =(1, 1, 1, 1, 1) x2 =(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...
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 = { _______ }