Worksheet 4February 2nd, 20091. IfAx=Aymustx=y? If so explain why, if not, find anAand twovectorsx6=ysuch thatAx=Ay2. Construct two 3×3 matricesAandBsuch thatAB= 0,A6= 0,B6= 0, andBA6= 0.3. Suppose forT:Rn→RnthatT(x) =bandT(y) =bfor somex6=y,canTmapRnontoRn.4. We know we can write any functionf:R2→R2asf(x, y) = (f1(x, y), f2(x, y)).Consider the linear transformationf(x) =AxwhereA=342-1.Write this function asf(x, y) = (f1(x, y), f2(x, y)).5. Matrix multiplication is not necessarily commutative.
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