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.
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).
† Let β={v1,v2,…,vn} be a basis for a vector space V
and T:V→V be a linear...
† Let β={v1,v2,…,vn} be a basis for a vector space V
and T:V→V be a linear transformation. Prove that [T]β is upper
triangular if and only if T(vj)∈span({v1,v2,…,vj}) j=1,2,…,n. Visit
goo.gl/k9ZrQb for a solution.
let v1=[1,0,10], v2=[0,1,0,1] and let W be the
subspace of R^4 spanned by v1 and v2....
let v1=[1,0,10], v2=[0,1,0,1] and let W be the
subspace of R^4 spanned by v1 and v2.
A. convert {v1,v2} into an orhonormal basis of W.
Basis =
B.find the projection of b=[-1,-2,-2,-1] onto W
C.find two linear independent vectors in R^4
perpendicular to W.
vectors =
Linear Algebra
Find the 2x2 matrix A of a linear transformation T: R^2->R^2
such that T(vi)...
Linear Algebra
Find the 2x2 matrix A of a linear transformation T: R^2->R^2
such that T(vi) = wi for i = 1,2.
v1=(4,3), v2=(5,4); w1=(-3,2), w2=(-3,-4)
Let W be a subspace of R^4 spanned by v1 =
[1,1,2,0] and v2 = 2,-1,0,4]....
Let W be a subspace of R^4 spanned by v1 =
[1,1,2,0] and v2 = 2,-1,0,4]. Find a basis for W^T
= {v is in R^2 : w*v = 0 for
w inside of W}
Find two vectors v1 and v2 whose sum is 〈1,3〉, where v1 is
parallel to 〈1,2〉...
Find two vectors v1 and v2 whose sum is 〈1,3〉, where v1 is
parallel to 〈1,2〉 while v2 is perpendicular to 〈1,2〉.
v1 =
and
v2 =
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?
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 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 = { _______ }