Question

I'm studying Linear Algebra. A Matrix A is a 3*3 matrix and it has 3 linear...

I'm studying Linear Algebra.

A Matrix A is a 3*3 matrix and it has 3 linear independent eigenvectors. The Matrix B has the same eigenvectors (but not necessarily the same eigenvalues). I'm supposed to prove that AB=BA. I'm given a clue that says: ,, Is it possible to diagonal A and B?''. I want to be clear that the matrixes are not given.
Thank you.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1


0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix,...
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix, and also have the same eigenvectors (but not necessarily the same eigenvalues), then  AB=BA.
Linear Algebra Conceptual Questions • If a subset of a vector space is NOT a subspace,...
Linear Algebra Conceptual Questions • If a subset of a vector space is NOT a subspace, what are the four things that could go wrong? How could you check to see which of these four properties aren’t true for the subset? • Is it possible for two distinct eigenvectors to correspond to the same eigenvalue? • Is it possible for two distinct eigenvalues to correspond to the same eigenvector? • What is the minimum number of vectors required take to...
The matrix [−1320−69] has eigenvalues λ1=−1 and λ2=−3. Find eigenvectors corresponding to these eigenvalues. v⃗ 1=...
The matrix [−1320−69] has eigenvalues λ1=−1 and λ2=−3. Find eigenvectors corresponding to these eigenvalues. v⃗ 1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ and v⃗ 2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ Find the solution to the linear system of differential equations [x′1 x′2]=[−13 20−6 9][x1 x2] satisfying the initial conditions [x1(0)x2(0)]=[6−9]. x1(t)= ______ x2(t)= _____
Matrix A is given as A = 0 2 −1 −1 3 −1 −2 4 −1...
Matrix A is given as A = 0 2 −1 −1 3 −1 −2 4 −1    a) Find all eigenvalues of A. b) Find a basis for each eigenspace of A. c) Determine whether A is diagonalizable. If it is, find an invertible matrix P and a diagonal matrix D such that D = P^−1AP. Please show all work and steps clearly please so I can follow your logic and learn to solve similar ones myself. I...
LINEAR ALGEBRA For the matrix B= 1 -4 7 -5 0 1 -4 3 2   ...
LINEAR ALGEBRA For the matrix B= 1 -4 7 -5 0 1 -4 3 2    -6 6    -4 Find all x in R^4 that are mapped into the zero vector by the transformation Bx. Does the vector: 1 0 2 belong to the range of T? If it does, what is the pre-image of this vector?
Prove that for a square n ×n matrix A, Ax = b (1) has one and...
Prove that for a square n ×n matrix A, Ax = b (1) has one and only one solution if and only if A is invertible; i.e., that there exists a matrix n ×n matrix B such that AB = I = B A. NOTE 01: The statement or theorem is of the form P iff Q, where P is the statement “Equation (1) has a unique solution” and Q is the statement “The matrix A is invertible”. This means...
Linear Algebra: Section 1.6 Applications Assume a corporation has a taxable income of $37,650,000. At this...
Linear Algebra: Section 1.6 Applications Assume a corporation has a taxable income of $37,650,000. At this income level, the federal income tax rate is 50%, the state income tax rate is 20%, and the local income tax is 10%. If each tax rate is applied to the total taxable income, the resulting tax liability for the corporation would be 80%. However it is customary to deduct taxes paid to one agency as expense before computing taxes for the other agencies....
Answer all of the questions true or false: 1. a) If one row in an echelon...
Answer all of the questions true or false: 1. a) If one row in an echelon form for an augmented matrix is [0 0 5 0 0] b) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. c) The solution set of b is the set of all vectors of the form u = + p + vh where vh is any solution...
1.    In a multiple regression model, the following coefficients were obtained: b0 = -10      b1 =...
1.    In a multiple regression model, the following coefficients were obtained: b0 = -10      b1 = 4.5     b2 = -6.0 a.    Write the equation of the estimated multiple regression model. (3 pts) b     Suppose a sample of 25 observations produces this result, SSE = 480. What is the estimated standard error of the estimate? (5 pts) 2.    Consider the following estimated sample regression equation: Y = 12 + 6X1 -- 3 X2 Determine which of the following statements are true,...
Asia’s e-commerce landscape has been booming in recent years. The swift adoption of smartphones and greater...
Asia’s e-commerce landscape has been booming in recent years. The swift adoption of smartphones and greater access to the internet has allowed consumers in the region to be a major force in the global digital economy. The expansion looks set to continue at a rapid pace. According to a November 2018 report by Fitch Solutions, e-commerce sales in the region are forecast to increase by 14.2% this year, with an estimated average annual increase of 14% over the medium term...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT