quiz3soln - Math 314H Solutions to Quiz 3 Let T R3 R4 be the linear transformation dened by x1 3x3 x1 x2 x2 = T x1 x2 3x3 x3 x1 2x2 3x3 1 Find the

quiz3soln - Math 314H Solutions to Quiz 3 Let T R3 R4 be...

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Math 314H — Solutions to Quiz 3 1. Find the standard matrix forT.Let{e1,e2,e3}be the standard basis forR3. Then 3. IsTone-to-one? Justify your answer. Tis one-to-one if and only if the systemAx=has only the trivial solution. But wesaw in the previous problem thatAx=bhas infinitely many solutions for at least onevectorb. Therefore,Ax=must have infinitely many solutions. 4. IsTonto? Again, justify your answer. Tis onto if and only if the columns ofAspanR4. This happens if and only if everyrow ofAhas a pivot element. But fromRwe see thatAhas only two pivots. Thus,Tis not onto.

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