Question: Linear AlgebraQuestion Help! -True/ false. lGive a brief explanationfeounterexample for each part. (i) If 'U E R is an eigenvector for A and B, then

Linear AlgebraQuestion Help!

-True/ false. lGive a brief explanationfeounterexample for each part. (i) If 'U E R\" is an eigenvector for A and B, then '1) is an eigenvector for A3. (ii) If A, p E C are eigenvalues of 51,3 respectively, then Ana is an eigenvalue for AB. [iii] If A E C is an eigenvalue for A, and c: E C, then (A + a)\" is an eigenvalue for A2 + 2eA + :21\". (iv) If A E R" is a. symmetric matrix with an eigenvalue with algebraic multiplicity 2, then Vi: E R\

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