The problem statement gives the correct answers for parts (a) and (b). The total number of roots of the characteristic polynomial is the dimension of the matrix: 6. The eigenvalues are the zeros of the characteristic polynomial, 3 (multiplicity 2), 6 (multiplicity 3), and -1.
(c) The matrix is not invertible when one or more eigenvalues is zero. None of yours are zero, so the matrix is invertible.
<u>Answer:</u>
<u>As the number of copies increases The dimension of images continues to decrease until reaching 0. </u>
<u>Step-by-step explanation:</u>
Remember, that the term dimension refers not to an unlimited/unending length but to a specific measurable length.
Therefore, as both copy machines reduces the dimensions of images that are run through the machines over time the dimensions of images would decrease until reaching 0; Implying that the dimension is so small to be invisible, in a sense becoming 0.
Answer:
D. d = 
Step-by-step explanation:
Use the distance formula: d = 
The two points are (6, -2) and (3, -9)
Plug the values into the formula:
d = 
Simplify
d = 
d = 
d =
I hope this helps :))
