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Mathematics

Mathematics 1229A/B

Vicki Olds

Fall

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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 thematrix 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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