MATH 2211 Midterm: Exam2210Sample3
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De ne the linear transformation t : r4 r3 so that x1 x2 x3 x4. 7 x1 + x2 x3 + x4. 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 = . De ne the linear transformations t : r4 r2 and s : r2 r4 so that. T x1 x2 x3 x4 x1 x2 + x3 + x4. X1 + x2 + 2x3 2x4 ] and s([ x1 x2 ]) = . Find the standard matrix of s t. b. ) Explain. c. ) find, if there is any, a vector v such that (s t)( v) = b where b = . De ne the linear transformations t : r2 r2 and s : r2 r2 so that. T ([ x1 x2 ]) = [ x1 + x2 x2. ] and s([ x1 x2 ]) = [
