If v is an eigenvector for a matrix A, can v be associated with two different...

If v is an eigenvector for a matrix A, can v be associated with two different eigenvalues? Prove your answer.

Expert Solution

cannot be associate with two eigenvalues of the matrix .

Proof : Suppose the eigenvector associates with two eigenvalues of which are and that is

, as is an eigen vector so it is non-zero .

a contradiction to .

Hence cannot be associate with two eigenvalues of the matrix .

.

If you have any doubt please comment .

Colby Messinger answered 2 years ago

1. What is the definition of an eigenvalue and eigenvector of a matrix? 2. Consider the...

1. What is the definition of an eigenvalue and eigenvector of a matrix? 2. Consider the nonhomogeneous equationy′′(t) +y′(t)−6y(t) = 6e2t. (a)Find the general solution yh(t)of the corresponding homogeneous problem. (b)Find any particular solution yp(t)of the nonhomogeneous problem using the method of undetermined Coefficients. c)Find any particular solution yp(t)of the nonhomogeneous problem using the method of variation of Parameters. (d) What is the general solution of the differential equation? 3. Consider the nonhomogeneous equationy′′(t) + 9y(t) =9cos(3t). (a)Findt he general...

Let v1 be an eigenvector of an n×n matrix A corresponding to λ1, and let v2,...

Let v1 be an eigenvector of an n×n matrix A corresponding to λ1, and let v2, v3 be two linearly independent eigenvectors of A corresponding to λ2, where λ1 is not equal to λ2. Show that v1, v2, v3 are linearly independent.

1. If (1, -1) is an eigenvector of A with associated eigenvalue -2, and (1, 1)...

1. If (1, -1) is an eigenvector of A with associated eigenvalue -2, and (1, 1) is an eigenvector of A with associated eigenvalue 4, then what the entries of A ,a11 , a12, a21 and a22 ? 2. If A has a repeated eigenvalue, the A definitely isn't diagonalizable. (True or False)

How can mutations in different genes be associated with a single disease?

Is there a relation between the determinant of the matrix associated to a linear mapping and...

Is there a relation between the determinant of the matrix associated to a linear mapping and the bijection of the mapping?

Create your own 2 × 2 payoff matrix for a two-person zero-sum game with v −...

Create your own 2 × 2 payoff matrix for a two-person zero-sum game with v − < v+. Solve your game (find a saddle point and the value of the game).

5. The structure of a two-way ANOVA study can be presented as a matrix with the...

5. The structure of a two-way ANOVA study can be presented as a matrix with the levels of one factor determining the rows and the levels of the second factor determining the columns. Factor A A1 A2 B1 Factor B B2 Factor A A1 A2 B1 Factor B B2 a. What are the three hypotheses that are evaluated in this study? b. With this structure in mind, describe the mean differences that are evaluated by each...

The results from a two-factor experiment can be presented in a matrix with the levels of...

The results from a two-factor experiment can be presented in a matrix with the levels of one factor forming the rows and the levels of the second factor forming the columns, with a separate sample in each of the matrix cells. Demonstrate this with your own example, and describe what is meant by the main effects for each factor and the interaction between factors based on the numbers that you choose to plug in for each one of the cells.

Explain in detain the different types of interferences associated with GF-AAS and the steps that can...

Explain in detain the different types of interferences associated with GF-AAS and the steps that can be taken to minimise their effects.

Why matrix can be multiplied by itself if and only if it is a square matrix?

Question