Consider the vector u1=(2,0,2), u2=(4,1,-1), u3=( 0,1,-5),
u4=(3,0,2)
a) Find the dimension and a basis for...
Consider the vector u1=(2,0,2), u2=(4,1,-1), u3=( 0,1,-5),
u4=(3,0,2)
a) Find the dimension and a basis for U= span{ u1,u2,u3,u4}
b) Does the vector u=(2,-1,4) belong to U. Justify!
c) Is it true that U = span{ u1,u2,u3} justify the answer!
find the basis and dimension for the span of each of
the following sets of vectors....
find the basis and dimension for the span of each of
the following sets of vectors.
a={[2,-1,1],[0,0,0],[-4,2,-2],[6,-3,3]}
basis=
dimension=
b={[3,3,3],[9,9,10],[21,21,23],[-33,-33,-36]}
basis=
dimension=
Consider the vector: u1=(1,1,1), u2= (2,-1,1), u3=(3,0,2),
u4=(6,0,4)
a)Plot the dimension and a basis for W=...
Consider the vector: u1=(1,1,1), u2= (2,-1,1), u3=(3,0,2),
u4=(6,0,4)
a)Plot the dimension and a basis for W= span {u1,u2,u3,u4}
b)Does the vector v= (3,3,1) belong to W? justify the
answer.
c) Is it true that W= span{ u3,u4} Justify answer.
a) Find a basis for W2 = {(x, y, z) ∈ R 3 : x +...
a) Find a basis for W2 = {(x, y, z) ∈ R 3 : x + y + z = 0} (over
R). Justify your answer. What is the dimension of W2?
b) Find a basis for W4 = {(x, y, z) ∈ R 3 : x = z, y = 0} (over
R). Justify your answer. What is the dimension of W4?
We have learned that we can consider spaces of matrices,
polynomials or functions as vector spaces....
We have learned that we can consider spaces of matrices,
polynomials or functions as vector spaces. For the following
examples, use the definition of subspace to determine whether the
set in question is a subspace or not (for the given vector space),
and why.
1. The set M1 of 2×2 matrices with real entries such that all
entries of their diagonal are equal. That is, all 2 × 2 matrices of
the form: A = a b c a
2....