MATH 2211 Midterm: Exam2210Sample1Ans
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De ne the linear transformation t : r2 r3 so that x2 ] 7 . Is t one-to-one? c. ) is t onto? d. ) if there is any, nd a vector v such that t( v) = b where b = . Because a x = 0 has only the trivial solution: no, t is not onto. Because, the number of pivot positions is less than the number of rows: no, there is no such vector v because we have. 0 0 1 where a row of the form [0 0 1] exists in the reduced form of the augmented matrix. De ne the linear transformations t : r2 r3 and s : r3 r2 so that. T ([ x1 x2 ]) = x1 2x2. = [ x1 + x2 x1 x2 ] . a. ) Find the standard matrix of s t. b. )
