Let S = { v 1 , v 2 , v 3 } be a set of linearly independent vectors in R 3 . Find a linear transformation T from R 3 into R 3 such that the set { T ( v 1 ) , T ( v 2 ) , T ( v 3 ) } is linearly dependent.
Let S = { v 1 , v 2 , v 3 } be a set of linearly independent vectors in R 3 . Find a linear transformation T from R 3 into R 3 such that the set { T ( v 1 ) , T ( v 2 ) , T ( v 3 ) } is linearly dependent.
Solution Summary: The author explains how to find a linear transformation T from R3 into
Let
S
=
{
v
1
,
v
2
,
v
3
}
be a set of linearly independent vectors in
R
3
. Find a linear transformation
T
from
R
3
into
R
3
such that the set
{
T
(
v
1
)
,
T
(
v
2
)
,
T
(
v
3
)
}
is linearly dependent.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
I want to learn this topic l dont know anything about it
Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
Chapter 6 Solutions
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