Question: please I need help with it. [C] Consider the following matrices in M22: (C.1) Determine value of a, for which the set, { A, ,

please I need help with it.

[C] Consider the following matrices in M22: (C.1) Determine value of a, for which the set, { A, , A2, A; } is a linearly dependent set. (C.2) Using the value of a identified in (C.1), express A, as a linear combination of Az and A3. (C.3) IfV is the vector space spanned by { A1, A2, As) what is the dimension of V? Again you are to use the value of a obtained in (C.1) Explain why the dimension is what you indicate? [D] Consider the following three bases for a vector space V, which is a subspace of C" (-00, 00): B, = {sin x, sin 2x , sin 3x} By = {sin x + sin 2x, sin x - sin 2x, sin 2x - sin 3x} B. = {sinx , sinx + sin 2x, sin x + sin 2x + sin 3x} (note: B, is the standard basis for V) Obtain the following transition matrices: Pp B, , Pp,-, , and Pp2-B

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