Stephen rode his bike 23.4865 miles On monday and 38.243 miles on Tuesday. How many miles did he ride in all
1 answer:
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A. False. Consider the identity matrix, which is diagonalizable (it's already diagonal) but all its eigenvalues are the same (1).
b. True. Suppose
is the matrix of the eigenvectors of 
, and 
is the diagonal matrix of the eigenvalues of :
Then
In other words, the columns of
are 
, which are identically 
, and these are the columns of 
.
c. False. A counterexample is the matrix
which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix
with eigenvalue
and eigenvector 
, where 
. But the matrix can't be diagonalized.
b. True. Suppose
Then
In other words, the columns of
c. False. A counterexample is the matrix
which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix
with eigenvalue
4.5 * (8-) + 36 = 102 - 2.5 * 27
4.5 * 8 - 36 = 102 - 2.5 * 27
36 - 36 = 102 - 2.5 * 27
36 - 36 = 102 - 67.5
36 - 36 = 34.5
Since we know 36 - 36 doesn't equal 34.5 its not true so there is NO ANSWER.
4.5 * 8 - 36 = 102 - 2.5 * 27
36 - 36 = 102 - 2.5 * 27
36 - 36 = 102 - 67.5
36 - 36 = 34.5
Since we know 36 - 36 doesn't equal 34.5 its not true so there is NO ANSWER.