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test 2 2008.pdf

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

Description
Thursday, November 6, 2008 CODE 111 Mathematics 1229A Page 1 Test 2 STUDENT NUMBER: 1. Consider the following systems of equations in the variables x,y and z. x y z x y z √ (i) x + 5y − z = 3 (ii) − + = 3 (iii) − + = 3 2 3 4 2 3 4 2 3 4 1 x(y + 2z) = 1 2 1 x − y + z = 3 x + 5 y − z = x + 5y − z = 3 3 x − y + z = √ 3 x − (y + 2z) = 1 2 3 4 Which of the above systems are linear in x,y and z? A: all of them B: (i) only C: (ii) only D: (iii) only E: none of them 2. Find the augmented matrix for the following system of linear equations. x − y − 2 = −z z = 2x ▯1 −1 −2 −1 ▯ ▯ 1 −1 −1 −2 ▯ ▯ 1 −1 1 2 ▯ A: 0 0 1 2 B: 2 0 1 0 C: 2 0 1 0 ▯ ▯ ▯ ▯ D: 1 −1 −2 −1 E: 1 −1 1 2 −2 0 1 0 −2 0 1 0 3. Which one of the following matrices is in row-reduced echelon form?           1 1 0 1 0 0 1 0 1 1 0 0 1 0 0           A: 0 1 0  B:  0 0 1  C: 0 1 1  D:  0 1 1  E: 0 0 0  0 0 1 0 0 1 0 0 0 0 0 1 0 0 1    −1 3 −1  4. Let A =  1 −4 2  and let B be the row-reduced echelon form of A. Then the 2 −6 2 ﬁrst row of B is ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ A: 1 0 −2 B: 1 0 2 C: 1 0 1 D: 1 0 0 E: 1 1 0 ▯ ▯ 1 1 y 5. Find all (x,y) so that the ma0 x 1 is in row-reduced echelon form. A: (0,1) only B: (1,0) onlyC: (1,1) and (0,0)D: (1,1) only E: (0,0) only Mathematics 1229A CODE 111 Thursday, November 6, 2008 Test 2 Page 2 6. The system of linear equations x1 − 2x 2 − 3x 3 + 2x 4 = 1 −x 1 + x2 + 3x 3 − 2x 4 = −2 −2x 1 + 4x 2 + 6x 3 − 4x 4 = −2 has A: no solutions B: exactly one solution C: a one-parameter family of solutions D: a two-parameter family of solutions E: a three-parameter family of solutions 7. Find the augmented matrix in row-reduced echelon form for the given system x − 2y − 3z = 1 −x + 2y + 3z = −1 x − 2y + 3z = −5 ▯ ▯ ▯ ▯ ▯ ▯ 1 −2 −3 1 1 −2 0 −2 1 0 0 2 A: −1 2 3 −1 B: 0 0 1 −1 C: 0 1 0 1 1 −2 3 −5 0 0 0 0 0 0 1 −1 ▯ ▯ ▯ ▯ 1 −2 −3 1 1 −2 −3 1 D: 0 0 0 0 E: 0 0 1 −1 0 0 −6 6 0 0 0 0   1 0 1 2 8. Let A = 0 1 −2 1  be the augmented matrix for a system of linear equations. The 0 0 0 0 solution to the system is A: (2,1,0)B: (0,0,0) C: (2 − t,1 + 2t,D: (2 − t,1 + 2t,E: there is no solution    1 0 2 8 9. Let A =  0 3 0 6 be the augmented matrix for a system of linear equations. 0 0 −1 −4 The solution to the system is A: (0,2,4) B: (8,2,4) C: (1,3,−1) D: (8,6,−4) E: there is no solution 10. Find the value(s) of k for which the system of linear equations with augmented matrix   1 0 0 3  0 1 3 2  has no solution. 0 2 k 4 A: k = 6 only B: k ▯= 6 C: k = −6 only D: k ▯= −6 E: no value of k Thursday, November 6, 2008 CODE 111 Mathematics 1229A Page 3 Test 2 11. ind the vale(s) of k for which the system of linear equations with augmented matrix 1 0 0 3  0 1 2 2    has exactly one solution. 0 k 4 4 A: k = −2 only B: k ▯= 2 C: k = 2 only D: k ▯= −2 E: no value of k   1 0 0 1   12. The matrix 0 1 0 1  is the augmented matrix for a linear system of three 0 0 k − 4 k + 2 equations in three unknowns x,y and z. Which of the following are true? (i) The system has no solution for k = 2. (ii) The system has exactly one solution for k ▯= ±2. (iii) The system has inﬁnitely many solutions for k = −2. A: (i) only B: (ii) only C: (iii) only D: all of them E: none of them 13. Describe the region (point, line, or plane), if any, that is the intersection of these planes. −x + 2y − z = 1 2x − 4y + 2z = −2 x − 2y + z = −1 A: a point B: a plane C: a line D: none of A,B or C E: all of A,B and C ▯ ▯   3 −2 7 8 4 14. If A = and B =  0 −1  then which of the following is not deﬁned? 0 8 1 −4 3 A: (BA) B: (A − B )T C: (A + B) D: (3A − 2B) E: (AB)T 15. For the matrices A and B from the previous question, what is AB
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