Question: Please answer in detail. 3-12 Let A be a 2 x 3 matrix for which multiplication by A transforms [2, 1, 1] onto [1, 1]

Please answer in detail.

3-12 Let A be a 2 x 3 matrix for which multiplication by A transforms [2, 1, 1] onto [1, 1] and [1, 1, 1] onto [1, -2]. a. / Determine, if possible, what multiplication by A transforms [0, 1, 1] to. [Hint: How does [o, 1, 1] relate to [1, 1, i] and [2, 1, 1]'?]) b. Suppose that it is also true that multiplication by A transforms [o, o, 1] onto [3, -5]. Determine what A transforms [2, 2, 3] to. c. /Find A. [Hint: The columns of A are AI, Al,, and Alg.]

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