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# Elementary Linear Algebra MATH 290

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This 5 page Class Notes was uploaded by Edgar Jacobi on Monday September 7, 2015. The Class Notes belongs to MATH 290 at Kansas taught by Satyagopal Mandal in Fall. Since its upload, it has received 94 views. For similar materials see /class/182372/math-290-kansas in Mathematics (M) at Kansas.

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Date Created: 09/07/15

Math 290 Practice Test 2 In class Part Satya Mandal Fall 2012 Maximum Points 60 October 117 2012 Student ID Name 1 Let 1 9 7 1 1 9 7 1 5 1 2 1 A 2571 B 534 284 O 2571 5 1 2 1 5 1 2 1 1 9 7 1 Find an elementary matrices EF so that B EA 0 FA 1 0 7 0 1 0 0 0 2 a Compute two elemenraty matrices E1 E2 such that EgElA I b Use the above to compute A71 Answer 2 Let A 3 Let HMOR OOW Q HHON OOHS a Compute the cofactors7 011 012 013 014 b Compute the detreminant of A by cofactor expansion 4 Let 1 2 3 713 0 3 7 9 A7 0 0 4 18 0 0 0 25 Compute determinant of A 5 Let 1 2 3 13 1 2 3 25 0 0 4 18 0 3 7 9 Compute the determinant of A7 by reducing it to a triangular matrix by elementary row operations 03 Let A and B be two suare matrices of same size Given 1A1 7 and 1B1 13 A D Compute lABl Compute lABTl Compute 1AAT1 Compute lAzl Compute l3Bl Compute lA lBl Compute lA lBTl Compute lAzB ll A 7 AA CLO A mi Tum AA II Consider the system 42 y 2 2 22 211 32 1 52 2y 22 4 of linear equations Use the determinant of the coef cient matrix to determine whether the system has unique solution 00 Consider the system 2 4y 2 1 52 1611 62 4 2x 4y 22 1 of linear equations Use the determinant of the coef cient matrix to determine whether the system has unique solution 2 9 Use Crarner7s rule to solve the following linear system 41 722 33 3 21 22 53 3 8x1 75 72m 0 Write your answer in matrix determinant form 10 Find the area of the triangle with vertices 7 7 72 2 3 71 Math 290 Fall 2012 Satya Mandal Due on October 117 2012 Test 2 Take home Part Maximum Points 15 1 Consider the elementary matrices E0 10a 100 001 E1010E2000E3010 001 001 100 with 0 7E 0 Compute the inverses of E1E2 E3 Answer Efl E31 Egl Prove7 for triangular matrices 111 0 0 0 A i 121 122 0 0 031 032 033 0 041 042 043 044 of order four7 A a11a22a33a44 Hint Use cofactor expansion7 by row Proof 3 Use the formula AB AHB 7 to prove that A H Proof

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