Eigenvalues and Eigenvectors of Linear Transformations In Exercises 45-48, consider the linear transformation T : R n → R n whose matrix A relative to the standard basis is given. Find (a) the eigenvalues of A , (b) a basis for each of the corresponding eigenspaces, and (c) the matrix A ' for T relative to the basis B ' , where B ' is made up of the basis vectors found in part (b). [ 0 2 − 1 − 1 3 1 0 0 − 1 ]
Eigenvalues and Eigenvectors of Linear Transformations In Exercises 45-48, consider the linear transformation T : R n → R n whose matrix A relative to the standard basis is given. Find (a) the eigenvalues of A , (b) a basis for each of the corresponding eigenspaces, and (c) the matrix A ' for T relative to the basis B ' , where B ' is made up of the basis vectors found in part (b). [ 0 2 − 1 − 1 3 1 0 0 − 1 ]
Solution Summary: The author explains how to calculate the eigenvalues of a given matrix.
Eigenvalues and Eigenvectors of Linear Transformations In Exercises 45-48, consider the linear transformation
T
:
R
n
→
R
n
whose matrix
A
relative to the standard basis is given. Find (a) the eigenvalues of
A
, (b) a basis for each of the corresponding eigenspaces, and (c) the matrix
A
'
for
T
relative to the basis
B
'
, where
B
'
is made up of the basis vectors found in part (b).
[
0
2
−
1
−
1
3
1
0
0
−
1
]
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.
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