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1. Recall that M2x2 is the set of 2 X 2 matrices, with addition and scalar multiplication defined by a b e f a + e b+ f + = and k: a d b = ka kb C d g h c+g d + h C kc kd (a) Prove that there exists a zero vector for M. 2x2. 20180220_000117.jpg (b) Prove, that there exists an additive inverse for all matrices in M2x2. 2. (a) Find the reduced row echelon form for the matrices 2 1 0 1 0 1 and B 1 2 2 A= = 1 3 3 Label any row operations used in the standard way. (b) Are A. B row equivalent? Why? (c) If A, B are row equivalent, find a sequence of row operations that converts A to B. (Hint: from part (a), you will have found row operations that change A, B into their reduced form. Make use of these operations or the operations done backward.) Label the row operations in the standard way.

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