7. For each of the following statements, indicate whether it is True or False: I

Question

7. For each of the following statements, indicate whether it is True or False: If ?' and ? 2 are distinct eigenvalues of a 2x2 matrix A. vi is any non-zero vector in the eigenspace of A corresponding to ?1 and v2 is any non-zero vector in the eigenspace of A corresponding to 12, then vi and v2 will be linearly independent If vi and v2 are linearly independent eigenvectors of a matrix A, then vi and v2 are in different eigenspaces corresponding to distinct eigenvalues of A An n × n matrix can have at most n real eigenvalues. a. b.

Explanation / Answer

a,b,c,d,e are true.

f is also false

g is true

h is false you can construct such matrix easily,

Similar matrix will have same number of eigen vector but they may not be same.

i is false.

j. false its easy to construct sucg matrix

k. True as the product of eigenvector is determinant

l. false.

m. false

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