MATH 2211 Midterm: Exam2210Sample4Ans
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De ne the linear transformation t : r3 r3 so that x1 x2 x3. 7 x1 + x2 + x3 x1 x2 + x3 x1 x2 x3 a. ) Explain. d. ) if there is any, nd a vector v such that t( v) = b where b = . 0 0 1: yes, t is one-to-one. Because a x = 0 has only the trivial solution: yes, t is onto. Because, the number of pivot positions is equal to the number of rows: yes, there is such vector v because we have. De ne the linear transformations t : r3 r3 and s : r3 r3 so that. 3x2 x3 x3 and s x1 x2 x3. 2x1 2x2 + x3 x2 3x3 x3 a. ) Find the standard matrix of s t. b. ) Find the standard matrix of t s. c. ) find, if there is any, a vector v such that (s t)( v) = b where b = .
