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Chapter 7: Q7-9E (page 383)

TRUE OR FALSE

9. There exists a diagonalizable 5脳5 matrix with only two distinct eigenvalues (over C).

Short Answer

Expert verified

True, that the diagonalizable 5脳5 matrix with only two distinct eigenvalues.

Step by step solution

01

Define the diagonalizable matrix

In linear algebra, the square matrix A is called diagonalizable or flawless if it is the same as the diagonal matrix.

If a square matrix A resembles a diagonal matrix, it is referred to as being diagonalizable in linear algebra.

02

Explanation for diagonalizable matrix

For example, A=1000001000001000002000002.

This matrix is already diagonal, so its diagonalizable, and its eigenvalues are the entries on its main diagonal, which are位1,2,3=1,位4,5=2

Hence, it is true that there exist only two distinct eigenvalues for a diagonalizable 5x5 marix.

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