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Chapter 7: Q7-23E (page 383)

If matrix A2 is diagonalizable, then matrix A must be diagonalizable as well.

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

Assume the matrix to find the eigenvalue

Consider the matrix,

A=0200

Hence, the matrix A is not diagonalizable, because its only eigenvalue is 位=0, with algebraic multiplicity 2 and geometric multiplicity 1.

Thus,

A2=0000

Which is a diagonal matrix, so it is diagonalizable.

Therefore, the given statement is false.

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