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 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)
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 {(1, 3, −4, 2),(2, 2, −4, 0),(1, −3, 2, 4)} is
linearly independent or...
Determine if {(1, 3, −4, 2),(2, 2, −4, 0),(1, −3, 2, 4)} is
linearly independent or not. Without using matrix.
Determine if the vectors v1= (3, 0, 3, 6),
v2 = ( 0, 2, 3, 1),...
Determine if the vectors v1= (3, 0, 3, 6),
v2 = ( 0, 2, 3, 1), and v3 = (0, 2, 2, 0 )
form a linearly dependent set in R 4. Is it a basis of
R4 ?
vectors u=(1,2,3), v=(2,5,7), w=(1,3,5) are linearly dependent
or independent? (using echelon form)
vectors u=(1,2,3), v=(2,5,7), w=(1,3,5) are linearly dependent
or independent? (using echelon form)
Determine all real numbers a for which the vectors
v1 = (1,−1,1,a,2)
v2 = (−1,0,0,1,0)
v3...
Determine all real numbers a for which the vectors
v1 = (1,−1,1,a,2)
v2 = (−1,0,0,1,0)
v3 = (1,2,a + 1,1,0)
v4 = (2,0,a + 3,2a + 3,4)
make a linearly independent set. For which values of a does the
set contain at least three linearly independent vectors?
Are vectors [1,0,0,2,1], [0,1,0,1,−4], and [0,0,1,−1,−1], and
[3,1,5,2,−6] linearly independent?
Are vectors v1=[−16,1,−39], v2=[2,6,3] and v3=[3,1,7]...
Are vectors [1,0,0,2,1], [0,1,0,1,−4], and [0,0,1,−1,−1], and
[3,1,5,2,−6] linearly independent?
Are vectors v1=[−16,1,−39], v2=[2,6,3] and v3=[3,1,7] linearly
independent?
If v1 and v2 are linearly independent vectors in vector space V,
and u1, u2, and...
If v1 and v2 are linearly independent vectors in vector space V,
and u1, u2, and u3 are each a linear combination of them, prove
that {u1, u2, u3} is linearly dependent.
Do NOT use the theorem which states, " If S = { v 1 , v 2 , . . . ,
v n } is a basis for a vector space V, then every set
containing
more than n vectors in V is linearly dependent."
Prove without...