Answer with explanation please A is an n times n matrix. Check the true statemen

Question

Answer with explanation please

A is an n times n matrix. Check the true statements below: A matrix A is not invertible if and only if 0 is an eigenvalue of A. To find the eigenvalues of A, reduce A to echelon form. A number c is an eigenvalue of A if and only if the equationn (A - cl)x = 0 has a nontrivial solution x. If Ax = lambda x for some vector x, then lambda is an eigenvalue of A. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is easy.

Explanation / Answer

A. False

0 is eigenvalue means: det(A)=0 hence A is nto invertible

B. False

That helps in finding soluiont to system of equations not finding eigenvalues

C. True.

D. True , by definition

E. Yes we just need to find Av and see if we get a multiple of v

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