MATH-205 Midterm: Bates MATH 205 041305jayawant205examsoln
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Check that you have 9 questions on four pages. Show all your work to receive full credit for a problem. Use this matrix to answer the following questions: 4 (a) find a basis for col a. [q]b~ f""l tl =: l-~ r p 1- =: l-i fo" P3 ~ rt j l\iv. i" . ~. l\ b) . t1-j tz,~ So !p:, is (b) define a linear transformation. T : jp>2- }r2by t(ao + alt + a2t2) = 1 cf~)=- f 2 (c) for the linear transformation t defined in part (b), the kernel of t is a subspace of jp>2 of dimension one. Find a basis for the kernel of t . (your answer to part you to find a basis. ) 10 asll h,y ~u t- t f>- s . 3. (10 points) determine a set is a subspace, find a basis and dimension of the subspace. if the following sets are subspaces of the appropriate vector spaces.
