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**bigwave** $\textsf{If A and b are $n \times n$ matrices. Mark each statemant T or F. Justify each answer}\\$

$\textit{ a. If $Ax=\lambda x$ for some vector x, then $\lambda$ is an eigenvalue of $A$}\\$

$\textit{ b. a matrix A is not invertible if and only if 0 is an eigenvalue of A}\\$

$\textit{ c. A number c is an eigenvalue of A iff the equation

$(A-c)x=0$ has a nontrival solution}\\$

$\textit{ d. Finding an eigenvector of A may be difficult

but checking whether a given vector is in fact an eigenvector is easy}\\$

$\textit{ e. To find the eigenvalue of A, reduce A to echelon form}$

ok barely had time to post this

but was having ???? with this

deeply appreciate help

having hard time in class