suppprobsIIwithanswers (3).pdf - Math 308 SUPPLEMENTARY...

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Math 308SUPPLEMENTARY CONCEPTUAL PROBLEMS IINeal KoblitzPlease note: Expect to find problems similar to the ones below on the midtermsand final exam. The assigned conceptual problems from the problem sets onthe syllabus (on the course webpage) are also similar to the types of problemsyou will find on the exams.II. Before second midterm:1. LetT1:IR2-→IR2be counterclockwise rotation through 60, and letT2:IR2-→IR2be expansion by 2 horizontally and by 3 vertically.Find the matrix for the llineartransformationT1followed byT2, and also for the linear transformationT2followed byT1.2. LetT1: IR2-→IR2be counterclockwise rotation through 45, and letT2: IR2-→IR2be reflection about the line through the origin that makes an angle of 22.5with thex1-axisin the first quadrant. Using geometrical reasoning, find the matrix forT1followed byT2,and also forT2followed byT1. In each case, can you find a simpler description of whatthe combined linear transformation does?3. LetT1be reflection about the linex2=x1, letT2:IR2-→IR2be counterclockwiserotation throughθ, and letT3:IR2-→

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