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if a is an nxn diagonalizable matrix then each vector in rn can be written as a linear cobination of eigenvectors of a

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KhiradAfaq

the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.

What is Diagonalizable matrix?

If there is an invertible matrix P and a diagonal matrix D such that

P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.

If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.

The given statement is false.

If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.

Hence, the given statement is false.

To know more about diagonalizable matrix, click on the link

https://brainly.com/question/15275426

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