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Chapter 7: Q36E (page 346)

Is matrix[0153]similar to [1243]?

Short Answer

Expert verified

The matrix A=0153 not similar to B=1243.

Step by step solution

01

Solving the matrix

Let,A=0153&B=1243IfA&BaresimilarthentrAmustbeequaltotrB
02

Find to similar or not

Here,trA=0+3=3trB=1+3=4trA鈮�trBHence,A&Barenotsimilar.Therefore,thefinalresultisA=0153notsimilartoB=1243.

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Most popular questions from this chapter

In all parts of this problem, let V be the linear space of all 2 脳 2 matrices for which [12]is an eigenvector.

(a) Find a basis of V and thus determine the dimension of V.

(b) Consider the linear transformation T (A) = A[12] from V to R2. Find a basis of the image of Tand a basis of the kernel of T. Determine the rank of T .

(c) Consider the linear transformation L(A) = A[13] from V to R2. Find a basis of the image of L and a basis of the kernel of L. Determine the rank of L.

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.

[5-421]

For which3脳3 matrices A does there exist a nonzero matrix M Such that AM=MD,where D=[200030004]Give your answer in terms of eigenvalues of A.

Find all2脳2matrices for which[12]is an eigenvector with associated eigenvalue 5 .

Find all2脳2matrices for whiche鈫�1=(10)is an eigenvector with associated eigenvalue 5.
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