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Chapter 7: Q7-21E (page 383)

TRUE OR FALSE

21. All diagonalizable matrices are invertible.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Define matrix

A table of numbers and symbols arranged in the form of rows and columns is known as a matrix.

02

Obtain whether the given statement is true or false

Consider the matrix,

A=2000

Hence, the matrix is diagonal already, so it is diagonalizable.

Since, the second column is 00, it is non-invertible.

Therefore, the given statement is false.

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Most popular questions from this chapter

Question: If a vector v鈫�is an eigenvector of both An脳n, Awith associated eigenvalue 位, what can you say aboutker(A-位滨n)?Is the matrixA-位滨ninvertible?

IfAis a matrix of rank 1, show that any non-zero vector in the image of Ais an eigenvector of A.

For a given eigenvalue, find a basis of the associated eigenspace. Use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable. For each of the matrices A in Exercises 1 through 20, find all (real) eigenvalues. Then find a basis of each eigenspace, and diagonalize A, if you can. Do not use technology

8((110022003)

If a vector v鈬赌is an eigenvector of both Aand B, isv鈬赌necessarily an eigenvector of A+B?

For a given eigenvalue, find a basis of the associated eigensspace .use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable.

For each of the matrices A in Exercise1 through 20,find all (real) eigenvalues. Then find a basis of each eigenspaces ,and diagonalize A, if you can. Do not use technology.

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