Decide whether the following set of vectors are linearly
independent or dependent. Justify the answer!
a)...
Decide whether the following set of vectors are linearly
independent or dependent. Justify the answer!
a) In R^3: v1=(0,2,3), v2=(3,-1,4), v3=(3,2,2)
b) In R^3: u1=(1,2,0), u2=(2,1,3), u3=(4,2,-1), u4=( 2,1,4)
c) In Matriz 2x2: A= | 1 6 | B= | 1 4 | C= | 1 4
|
|-1 4 |, | 3 2 |, | 2 -4 |
Determine whether the given functions are linearly dependent or
linearly independent.
f1(t) =
4t − 7,...
Determine whether the given functions are linearly dependent or
linearly independent.
f1(t) =
4t − 7,
f2(t) =
t2 + 1,
f3(t) =
6t2 − t,
f4(t) =
t2 + t + 1
linearly dependentlinearly independent
If they are linearly dependent, find a linear relation among them.
(Use f1 for f1(t),
f2 for f2(t),
f3 for f3(t), and
f4 for f4(t).
Enter your answer in terms of f1,
f2, f3, and
f4. If the system is independent, enter
INDEPENDENT.)
Determine if vectors are linearly dependent or
independent:
1. (1,2), (-1,-3)
2. (2,-1,4),(4,-2,7),(1,5,8)
3. (-3,4,2),(7,-1,3),(1.1.8)
Determine if vectors are linearly dependent or
independent:
1. (1,2), (-1,-3)
2. (2,-1,4),(4,-2,7),(1,5,8)
3. (-3,4,2),(7,-1,3),(1.1.8)
Determine whether the given functions are linearly dependent or
linearly independent.
f1(t) =
2t − 9,...
Determine whether the given functions are linearly dependent or
linearly independent.
f1(t) =
2t − 9,
f2(t) =
2t2 + 1,
f3(t) =
9t2 + t
If they are linearly dependent, find a linear relation
among them. (Use f1 for f1(t), f2 for f2(t), and f3 for f3(t).
Giveyour answer in terms of f1, f2, and f3.)
Show that the set is linearly dependent by finding a nontrivial
linear combination of vectors in...
Show that the set is linearly dependent by finding a nontrivial
linear combination of vectors in the set whose sum is the zero
vector. (Use
s1, s2, and s3, respectively,
for the vectors in the set.)
S = {(5, 2), (−1, 1), (2, 0)}
a) (0, 0) =
b) Express the vector s1 in the set as a
linear combination of the vectors s2 and
s3.
s1 =
if
{Av1,Av2,...,
Avk} is linearly dependent set
of vectors in Rn and A is an nxn...
if
{Av1,Av2,...,
Avk} is linearly dependent set
of vectors in Rn and A is an nxn invertible
matrix, the
{v1,v2,...vk}
is also a linearly dependent set of vectors in Rn
Determine if vectors are linearly dependent or
independent:
1. (1,-2,1,1),(3,0,2,-2),(0,4,-1,-1),(5,0,3,-1)
2. (1.-1.2),(4,0,0),(-2,3,5),(7,1,2)
Determine if vectors are linearly dependent or
independent:
1. (1,-2,1,1),(3,0,2,-2),(0,4,-1,-1),(5,0,3,-1)
2. (1.-1.2),(4,0,0),(-2,3,5),(7,1,2)
Let
S={v1,...,Vn} be a linearly dependent set.
Use the definition of linear independent / dependent to...
Let
S={v1,...,Vn} be a linearly dependent set.
Use the definition of linear independent / dependent to show that
one vector in S can be expressed as a linear combination of other
vectors in S.
Please show all work.