1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Murrr4er [49]
3 years ago
13

) a, p and d are n×n matrices. check the true statements below:

Mathematics
1 answer:
BigorU [14]3 years ago
7 0
A. False. Consider the identity matrix, which is diagonalizable (it's already diagonal) but all its eigenvalues are the same (1).

b. True. Suppose \mathbf P is the matrix of the eigenvectors of \mathbf A, and \mathbf D is the diagonal matrix of the eigenvalues of \mathbf A:


\mathbf P=\begin{bmatrix}\mathbf v_1&\cdots&\mathbf v_n\end{bmatrix}

\mathbf D=\begin{bmatrix}\lambda_1&&\\&\ddots&\\&&\lambda_n\end{bmatrix}

Then

\mathbf{AP}=\begin{bmatrix}\mathbf{Av}_1&\cdots&\mathbf{Av}_n\end{bmatrix}=\begin{bmatrix}\lambda_1\mathbf v_1&\cdots&\lambda_n\mathbf v_n\end{bmatrix}=\mathbf{PD}

In other words, the columns of \mathbf{AP} are \mathbf{Av}_i, which are identically \lambda_i\mathbf v_i, and these are the columns of \mathbf{PD}.

c. False. A counterexample is the matrix

\begin{bmatrix}1&1\\0&1\end{bmatrix}

which is nonsingular, but it has only one eigenvalue.

d. False. Consider the matrix

\begin{bmatrix}0&1\\0&0\end{bmatrix}

with eigenvalue \lambda=0 and eigenvector \begin{bmatrix}k&0\end{bmatrix}^\top, where k\in\mathbb R. But the matrix can't be diagonalized.
You might be interested in
????? helllppppp.....
julia-pushkina [17]

Answer:

The answer is : √3/2

Step-by-step explanation:

Sin 60 = √3/2

6 0
3 years ago
Mr. Frankel bought 7 tickets to a puppet show and spent $43. He bought a combination of child tickets for $4 each and adult tick
pav-90 [236]
A + C = 7
$9(A) + $4(C) = $43
8 0
3 years ago
Read 2 more answers
Find the vertex of the parabola whose equation is y = x 2 + 8x + 12. (-4, 12) (-4, -4) (0, -6)
dsp73

The answer should be (-4,-4)


Good luck<3

5 0
3 years ago
Whats is the answer to the equation 10+43
liraira [26]

Answer:

53

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Each block in Ton’s neighborhood is 2/3 mile long if he walk 4 1/2 blocks how far does he walk?
nataly862011 [7]

if each block is 2/3 miles long, and he walks 4 1/2 blocks, we can simply multiply to two. It looks like this:

(2/3)(4 1/2)

to multiply, make 4 1/2 into an improper fraction and multiply normally

(2/3)(9/4)

Ton walks 3 miles total.

3 0
3 years ago
Other questions:
  • These plots show the number of kilometers a group of students at Middleton Middle School and at Westwood Middle School travel to
    12·2 answers
  • How do u solve 1736÷56 step by step
    13·2 answers
  • Find the range of ƒ(x) = –x + 4 for the domain {–3, –2, –1, 1}.
    5·2 answers
  • How many squares would have to be shaded so that 1/6 of the shape is shaded?
    7·1 answer
  • Find x, y and z. <br><br> A. B. C. Or D.
    7·2 answers
  • Paul runs 4.8 km every morning. How many feet are in 4.8 km, given that 1 mile = 1.609 km and 1 mile = 5,280 feet?
    12·2 answers
  • Someone pls help me due in 30 min. Given that x and y show inverse variation, complete the table.
    9·1 answer
  • Please help asap.........!!!!!!!!!
    5·1 answer
  • What number would you add to both sides of x² + 7x = 4 to complete the square?
    12·1 answer
  • 9. What is the relationship between the estimates you found for the lengths of the two equators?4 grade student
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!