Linear Algebra Sample Exam 1 - Math 136 Sample Final Exam 1...

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Math 136 - Sample Final Exam 1NOTE:The questions on this exam does not exactly reflect which questions will be on this termsexam. That is, some questions asked on this exam may not be asked on our exam and there maybe some questions on our exam not asked here.1.Short Answer Problemsa) Find the inverse ofA=12-13.b) LetL1, L2:R3R3whereL1is a reflection in thex2x3-plane andL2is a reflectionin thex1x2-plane. Find the matrices forL1,L2andL2L1.c) State the definition of and eigenvalue and eigenvector of a matrixA.d) LetAbe ann×nmatrix such thatA2= 0. Prove that the columnspace ofAisa subset of the nullspace ofA.2.LetA=10-5620.a) Find the reduced row echelon formBofA.b) WriteAas a product of elementary matrices andB.3.LetCbe a square matrix whose nullspace ist1111tR.

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