Find an equation for the plane that
(a) is perpendicular to v=(1,1,1)v=(1,1,1) and passes through
(1,0,0).(1,0,0)....
Find an equation for the plane that
(a) is perpendicular to v=(1,1,1)v=(1,1,1) and passes through
(1,0,0).(1,0,0).
(b) is perpendicular to v=(1,2,3)v=(1,2,3) and passes through
(1,1,1).(1,1,1).
(c) is perpendicular to the line
l(t)=(5,0,2)t+(3,−1,1)l(t)=(5,0,2)t+(3,−1,1) and passes through
(5,−1,0).(5,−1,0).
(d) is perpendicular to the line
l(t)=(−1,−2,3)t+(0,7,1)l(t)=(−1,−2,3)t+(0,7,1) and passes through
(2,4,−1).
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): compute projw j if u1=[-7,1,4] u2=[-1,1,-2],w=span{u1,u2}.
(u1 and u2 are orthogonal)
B): let u1=[1,1,1], u2=1/3...
A): compute projw j if u1=[-7,1,4] u2=[-1,1,-2],w=span{u1,u2}.
(u1 and u2 are orthogonal)
B): let u1=[1,1,1], u2=1/3 *[1,1,-2] and w=span{u1,u2}.
Construct an orthonormal basis for w.
Given f(x,y) = 2y/sqrt(x) , find a unit vector u =
(u1,u2) such that Duf(1,3) =...
Given f(x,y) = 2y/sqrt(x) , find a unit vector u =
(u1,u2) such that Duf(1,3) = 0 and
u1 > 0
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!
Let U and W be subspaces of a nite dimensional vector space V
such that U...
Let U and W be subspaces of a nite dimensional vector space V
such that U ∩ W = {~0}. Dene their sum U + W := {u + w | u ∈ U, w ∈
W}.
(1) Prove that U + W is a subspace of V .
(2) Let U = {u1, . . . , ur} and W = {w1, . . . , ws} be bases
of U and W respectively. Prove that U ∪ W...
Homework #2
a) Find a vector perpendicular to the vectors 2i + 3j-k and 3i +...
Homework #2
a) Find a vector perpendicular to the vectors 2i + 3j-k and 3i +
k
b)Find the area of the triangle whose vertices are (2, -1,1),
(3,2,1) and (0, -1,3)
c)Find the volume of the parallelepiped with adjacent axes PQ,
PR, and PS with P (1, -2.2), Q (1, -1.3), R (1,1,0), S (1,2,3 )
Vectors u1= [1,1,1] and u2=[8,-7,-1] are
perpendicular. Find the orthogonal projection of
u3=[65,-19,-31] onto the plane...
Vectors u1= [1,1,1] and u2=[8,-7,-1] are
perpendicular. Find the orthogonal projection of
u3=[65,-19,-31] onto the plane spanned by u1
and u2.