1)
Find a basis for the column space of A=
2 -4 0 2 1
-1...
1)
Find a basis for the column space of A=
2 -4 0 2 1
-1 2 1 2 3
1 -2 1 4 4
2) Are the following sets vector subspaces of R3?
a) W = {(a,b,|a|) ∈ R3 | a,b ∈ R}
b) V = {(x,y,z) ∈ R3 | x+y+z =0}
Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5,...
Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5, −2, 8, 1).
Find the vector x that satisfies 2u − ||v||v = 3(w − 2x).
Suppose A is the matrix for T: R3 → R3 relative to the standard
basis.
Find...
Suppose A is the matrix for T: R3 → R3 relative to the standard
basis.
Find the diagonal matrix A' for T relative to the basis B'. A =
−1 −2 0 −1 0 0 0 0 1 , B' = {(−1, 1, 0), (2, 1, 0), (0, 0, 1)}
10 Linear Transformations. Let V = R2 and W = R3. Define T: V →
W...
10 Linear Transformations. Let V = R2 and W = R3. Define T: V →
W by T(x1, x2) = (x1 − x2, x1, x2). Find the matrix representation
of T using the standard bases in both V and W
11 Let T :R3 →R3 be a linear transformation such that T(1, 0, 0)
= (2, 4, −1), T(0, 1, 0) = (1, 3, −2), T(0, 0, 1) = (0, −2, 2).
Compute T(−2, 4, −1).
If A=[(1, 2,1)
(2, 0, 0)
(0, 5, 0)]
A: R3->R3
1) Find the row reduced...
If A=[(1, 2,1)
(2, 0, 0)
(0, 5, 0)]
A: R3->R3
1) Find the row reduced echelon form of A
2) Find the image of A
3) Find a nonzero vector in ker(A)
1. V is a subspace of inner-product space R3,
generated by vector
u =[2 2 1]T...
1. V is a subspace of inner-product space R3,
generated by vector
u =[2 2 1]T and v
=[ 3 2 2]T.
(a) Find its orthogonal complement space V┴ ;
(b) Find the dimension of space W = V+ V┴;
(c) Find the angle θ between u and
v and also the angle β between u
and normalized x with respect to its 2-norm.
(d) Considering v’ =
av, a is a scaler, show the
angle θ’ between u and...
Determine the quadratic regression for the data.
{(1, 5), (3, 4), (4, 1), (5, 2), (7,...
Determine the quadratic regression for the data.
{(1, 5), (3, 4), (4, 1), (5, 2), (7, 4)}1, 5, 3, 4, 4, 1, 5, 2,
7, 4
Explain how you got your answers. Round to the nearest
hundredth.
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.
(a) Use the Gram-Schmidt process on the basis {(1, 2, 2),(1, 2,
3),(4, 3, 2)} of...
(a) Use the Gram-Schmidt process on the basis {(1, 2, 2),(1, 2,
3),(4, 3, 2)} of R ^3 find an orthonormal basis.
(b) Write the vector v = (2, 1, −5) as a linear combination of
the orthonormal basis vectors found in part (a).