For parts ( a ) − ( c
) , let u = 〈 2 ,...
For parts ( a ) − ( c
) , let u = 〈 2 , 4 , − 1 〉 and v = 〈 4 , − 2 , 1 〉 .
( a ) Find a unit
vector which is orthogonal to both u and v .
( b ) Find the vector
projection of u onto v .
( c ) Find the scalar
projection of u onto v .
For parts ( a ) − (...
U= [2,-5,-1] V=[3,2,-3] Find the orthogonal projection of u onto
v. Then write u as the...
U= [2,-5,-1] V=[3,2,-3] Find the orthogonal projection of u onto
v. Then write u as the sum of two orthogonal vectors, one in
span{U} and one orthogonal to U
Consider the following.
u =
−6, −4, −7
, v =
3, 5, 2
(a) Find the...
Consider the following.
u =
−6, −4, −7
, v =
3, 5, 2
(a) Find the projection of u onto
v.
(b) Find the vector component of u orthogonal to
v.
Let u = [-2,1,3,1] and let v = [1,4,0,1]. a. Determine the
projector P1 that projects...
Let u = [-2,1,3,1] and let v = [1,4,0,1]. a. Determine the
projector P1 that projects onto the subspace S1 spanned by the
vector u. What isthe rank of P1? b. Determine the projector that
projects onto the orthogonal complement of S1. c. Determine the
projector P2 that projects onto the subspace S2 spanned y the
vectors {u,v}. What is the rank of P2? d. Determine an orthogonal
projector that projects onto the orthogonal complement of S2. e.
Verify that...
1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2].
Let w⃗ = 3⃗u−⃗v. Express w⃗ as...
1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2].
Let w⃗ = 3⃗u−⃗v. Express w⃗ as a linear combination of the vectors
[4, 0, 1] and [−1, 3, −2].
2. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 3,
||⃗u − ⃗v|| = 5, and that⃗u.⃗v = 1. What is ||⃗v||?.
3. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 5
and that ||⃗v|| = 2. Show that ||⃗u −...
Find the following for the vectors u= -10+9j+√3k and v=
10i-9j-√3k.
a) v*u, |v|, and |u|....
Find the following for the vectors u= -10+9j+√3k and v=
10i-9j-√3k.
a) v*u, |v|, and |u|.
b) the cosine of the angle between v and u.
c) the scalar component of u in the direction of v
d) the vector projvu
Let u=[6,2 ], v=[3,3 ], and b=[4,1 ]. Find
(x⋅u+y⋅v-b)×2 u, where x,y are scalars.
Let u=[6,2 ], v=[3,3 ], and b=[4,1 ]. Find
(x⋅u+y⋅v-b)×2 u, where x,y are scalars.