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# test 2 2010.pdf

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School
Department
Mathematics
Course
Mathematics 1229A/B
Professor
Vicki Olds
Semester
Fall

Description
Friday, November 5, 2010 CODE 111 Mathematics 1229A Page 1 Test 2 PART A (17 marks) NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE INDICATED ON THE SCANTRON SHEET. YOU SHOULD ALSO CIRCLE YOUR ANSWERS IN THIS BOOKLET. 1 1. Which of the following equations are linear? mark (i) x1− 2x3 = x 2 4x 3 (ii) x1+ x2 3− 2x4 = 17 (iii) 1 + 2 + 3 + 4 = 5 A: none of them B: (i) only C: (ii) onlyD: (iii) onlyE: (i) and (iii) only 1 2. Which one of the given vectors is a solution to the syx2+ x3 = 3 ? mark x1− x 2 = −3 2x1+ 2x2+ x3 = 3 A: (1,1,−1) B: (−1,2,1) C: (3,3,−3) D: (0,3,0) E: (−2,4,1) 1 3. Find the augmented matrix for the following system of linear equations. mark 3x1− 2x2 + x4 = 6 x1 − 3x3− 2x4 = 6 x2+ x 3 x 4 = 0. ▯ ▯ ▯ ▯ ▯ ▯ 3 2 0 1 6 3 −2 1 6 3 −2 0 1 6 A: 1 0 3 2 6 B: 1 −3 −2 6 C: 1 0 −3 −2 6 0 1 1 1 0 1 1 1 0 0 1 1 1 0   ▯ ▯ 1 0 0 5 30 3 2 0 1  11 11  D: 1 −3 −2 0 E:  0 1 0 11 11  1 1 1 0 9 12 0 0 1 11 − 11 1 4. Which of the following matrices are in row-reduced echelon form? mark     0 0 1 2 0 1 0 0 4 0 P =  1 0 0 4 0  Q =  0 1 0 3 3      0 1 0 3 3 0 0 1 2 0     1 0 0 4 0 1 4 3 0 0     R =  0 1 0 3 1  S =  0 1 2 0 1  0 0 1 2 0 0 0 1 0 0 A: R only B: Q and R only C: P, Q and R only D: P and S only E: S only   1 1 1   1 5. Find the row-reduced echelon form of thematrix 0 . mark −1 1 −3           1 0 2 1 0 0 1 1 1 1 0 0 1 1 1           A: 0 1 −1  B:  0 2 0  C: 0 0 0  D:  0 1 0  E: 0 1 −1  0 0 0 0 0 −3 0 0 0 0 0 1 0 0 0 Mathematics 1229A CODE 111 Friday, November 5, 2010 Test 2 Page 2 1 6. Find the value of k for which the matrix shown below DOES NOT row-reduce to the 3×3 mark identity matrix.   1 4 2    0 1 1  2 −1 k A: 1 B: 2 C: −2 D: 5 E: −5   1 2 0 0 0   1 7. Find the solution of the system whose augmented atrix is0 15. mark  0 0 0 1 5  0 0 0 0 0 A: (1 − 5t,2 − 5t,1 − 5t,−2 −B: (5 − t,2,5 + 2t,C: (5,5,5,0) D: (−2t,t,15,5) E: (1,2 − 5t,1,1 − 5t)    3x1 − 2x 2 + x 3 = 16  1 8. The system of linear equations1 + x2 − x 3 = 1 has mark   2x1 − x 3 = 16 A: no solutions B: exactly one solution C: a one-parameter family of solutioD: a two-parameter family of solutions E: a three-parameter family of solutions ▯ ▯ x1+ x2+ x3= 7 mark 9. The system of linear equatix + x + x = 19 has 1 2 3 A: no solutions B: exactly one solution C: a one-parameter family of solutioD: a two-parameter family of solutions E: a three-parameter family of solutions ▯ ▯  ▯ ▯ 1 1 −1 x 1 1 10. Solve the system of equations represented by   = mark 2 0 −4  y  2 z A: (1 + 2t,−t,t)B: (1,2) C: (5,1,−9) D: (1 − t,2 − 4t)E: (1 + 2t,0,t) 1 11. If F is a 1 × 4 matrix and G is a 4 × 2 matrix then F FG is a mark A: 1 × 2 matrixB: 2 × 2 matrix C: 3 × 2 matrix D: 4 × 2 matrixE: undeﬁned 1 12. Find the value 34in the following: mark      3 1 2 5 2 9 3 a11 a12 a13 a14  2 1 1  1 −1 1 −1  =  a21 a22 a23 a24  4 1 −3 0 1 2 2 a31 a32 a33 a34 A: 1 B: 2 C: 3 D: 4 E: 5 Friday, November 5, 2010 CODE 111 Mathematics 1229A Page 3 Test 2 ▯ ▯ ▯ ▯ 2 1 1 1 −1 T 1
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