1. Recall that M2x2 is the set of 2 X 2 matrices, with addition and scalar multiplication
a + e b+ f
a d b =
c+g d + h
(a) Prove that there exists a zero vector for M. 2x2.
(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
1 3 3
Label any row operations used in the standard
(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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