summer2018_Math1300_Quiz2A-soln - Laboratory Quiz#2A Time 20 minutes Name Student ID Answer all questions and show all your work in the provided

# summer2018_Math1300_Quiz2A-soln - Laboratory Quiz#2A...

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Laboratory Quiz #2A Time: 20 minutes Name: Student ID Answer all questions and show all your work in the provided space. No calculators allowed. ( Total Marks: 20) . 1. Let A = 3 1 0 - 1 2 1 0 - 1 2 , and adj( A ) = 5 a b 2 6 - 3 1 3 7 . (a)  Find det( A ) using row 1. Solution: det( A ) = (3) 2 1 - 1 2 - (1) - 1 1 0 2 = (3)(5) - (1)( - 2) = 17. MARKS: 1 mark for the each determinant 1 mark for the result (b)  Find (d)FindA-1. 1
2.Given thatabcdefghi= 7, deduce the value of the determinanta+ 3db+ 3ec+ 3f-2g-2h-2idef. 1 mark for the second equality1 mark for the third equality1 mark for the result 3.Use Cramer’s rule to findx1in the system3x1+ 4x2= 7-2x1+ 5x2=-2 Solution:x1=det(A1)det(A)1 mark=74-2534-251 mark=(7)(5)-(4)(-2)(3)(5)-(4)(-2)=43231 mark 4.LetAandBbe 3×3 invertible matrices such that det(A) = 2 and det(B) = 3. Find det((2B)A-1). Solution:det((2B)A-1) = det(2B) det(A-1)1 mark= det(2B)1det(A)1 mark= 23det(B)1det(A)1 mark=(8)(3)2= 12.1 mark 2
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