20f-su98-final

20f-su98-final - Final Exam, Math 20F July 31, 1998 Section...

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Final Exam, Math 20F Signature July 31, 1998 Section # Name (Print, with non-eraseable pen) This exam is closed book, closed notes and closed calculator. Please work alone, and show and explain your work and justify your answers–give clear explanation in plain language combined with suitable equations. Each problem is worth 55 points for a total of 10 × 55=550 points. 1. Let 230100 010200 000100 0000 cd be the echelon form of the augmented matrix of the system Ax = b , with A a4 × 5 matrix. Given the general solution in the 3 cases: c 6 =0 6 = d ; c 6 =0= d ; and c 6 = d . 2. For A = 123 01 - 1 0 - 11 give a basis of Null( A ) and a basis of Col( A ). 3. Find the general solution of the system 2 x 1 +3 x 2 +11 x 3 +6 x 4 =11 x 2 x 3 +5 x 4 =6 x 1 + x 2 +2 x 3 =1 . 4. Find the inverse A - 1 of A = 1 - 21 4 - 77 - 36 - 2 . 5. Find a basis of the vector space spanned by the 4 vectors. 1 0 0 1 , 1 - 1 1 - 2 , - 1 2 - 1 6 , - 4 3 - 3 5 . 6. Compute the determinant of A = 121 1 - 131 - 1 - 112 3 - 111 - 1
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20f-su98-final - Final Exam, Math 20F July 31, 1998 Section...

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