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Chapter 7: Q4E (page 323)

Is v鈬赌an eigenvector of 7 A? If so, what is the eigenvalue?

Short Answer

Expert verified

Yes. And the required given value is 7位.

Step by step solution

01

Define the eigenvector

Eigenvector: An eigenvector of A is a nonzero vector v in Rnsuch that Av=位惫, for some scalar位 .

02

Finding the eigenvalue of 7 A

If v鈬赌 is an Eigen vector of A this means that

Av鈬赌=位v鈬赌If we now look at 7A we will have;

localid="1659531405021" 7Av鈬赌=7Av鈬赌=7位v鈬赌

Thus, v鈬赌is an Eigen vector of 7A with Eigen value7位.

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Most popular questions from this chapter

Two interacting populations of coyotes and roadrunners can be modeled by the recursive equations

c(t + 1) = 0.75r(t)

r(t + 1) = 鈭�1.5c(t) + 2.25r(t).

For each of the initial populations given in parts (a) through (c), find closed formulas for c(t) and r(t).

(a)c(0)=100,r(0)=200(b)c(0)=r(0)=100(c)c(0)=500,r(0)=700

find an eigenbasis for the given matrice and diagonalize:

A=19[82-2255-244]

Representing the orthogonal projection onto the planex-2y+2z=0

Find all the polynomials of degree 鈮�2[a polynomial of the formf(t)=a+bt+ct2] whose graph goes through the points (1,3) and (2,6) , such thatrole="math" localid="1659541039431" f'(1)=1[wheref'(1)denotes the derivative].

Suppose v鈨�Supposeis an eigenvector of the n脳nmatrix A, with eigenvalue 4 . Explain why v鈨�is an eigenvector of A2+2A+3In.What is the associated eigenvalue?

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[-3040-10-273]
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