Maths 2 week 1 important questions

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1. Q4Let u=(2, 1, 4) and v=(2, 4, 4). Find , where is the angle between u and v (2 decimal plac
2. Q5Let u=(0, -3) and v=(5, -2). The projection of u on v is t, ,v. Find t (2 decimal places).
3. Q6Let u=(-4, -1, 4) and v=(-1, 4, 2). Find component number 2 of 2u-2v.
4. Q7The vector w=(3, 4) is divided by its length to get a unit vector. What is the first compo
5. Q8Let u=(3, 0, 2) and v=(5, 2, -3). The vectors u and v are
6. Q9Let u=(3, -3) and v=(-3, -2). Find the dot product u v.
7. Q10Let u=(0, 4, 3) and v=(-4, 0, 2). Find |u|2, the square of the length of u.
8. Q11Let u=(k, 5) and v=(-2, 2). Find k so that u and v are perpendicular (orthogonal).
9. Q12Let u=(-1, 5, 1) and v=(3, 1, 1). Find , where is the angle between u and v (2 decimal pla
10. Q13Let u=(5, -2) and v=(1, -2). The projection of u on v is t, ,v. Find t (2 decimal places).
11. Q14Let u=(4, -1, 3) and v=(5, 0, 0). Find component number 1 of -1u-3v.
12. Q15The vector w=(5, 12) is divided by its length to get a unit vector. What is the first comp
13. Q16Let u=(0, 3, 1) and v=(2, 3, 0). The vectors u and v are
14. Q17Let A=(matrix) and B=(matrix). Find the entry in row 2, column 2 of…
15. Q18Let A=(matrix) and B=(matrix). F…
16. Q19Let A=(matrix) and B=(matrix). Find the entry in row 1, column 1 o…
17. Q20Let A=(matrix) and B=(matrix). Find the entry in row 1, column 2 …
18. Q21Find the trace (sum of the diagonal entries) of A=(matrix).
19. Q22For A=(matrix), find the entry in row 1, column 1 of A2.
20. Q23Let A=(matrix) and B=(matrix). Which statement is correct?
21. Q24Let A=(matrix) and B=(matrix). Find the entry in row 2, column 2 …
22. Q25Let A=(matrix) and B=(matrix). Find the entry in …
23. Q26Let A=(matrix) and B=(matrix). Find the entry in row 2, column 2 of…
24. Q27Let A=(matrix) and B=(matrix). Find the entry in row 1, column 1 …
25. Q28Find the trace (sum of the diagonal entries) of A=(matrix).
26. Q29For A=(matrix), find the entry in row 2, column 1 of A2.
27. Q30Let A=(matrix) and B=(matrix). Which statement is correct?
28. Q31Find (matrix).
29. Q32Find the determinant of A=(matrix). Select all the true statements about the val…
30. Q33Find the determinant of A=(matrix).
31. Q34Find (matrix).
32. Q35Find the determinant of A=(matrix).
33. Q36Find the determinant of A=(matrix).
34. Q37Find (matrix).
35. Q38Find the determinant of A=(matrix).
36. Q39Find the determinant of A=(matrix).
37. Q40Find (matrix). Select all the true statements about the value asked for.
38. Q41Find the determinant of A=(matrix).
39. Q42Find the determinant of A=(matrix).
40. Q43A is a 22 matrix with A=-1. Find (2A).
41. Q44A and B are 44 matrices with A=-1 and B=3. Find (AB).
42. Q45A is an invertible 44 matrix with A=-2. Find (A-1) (2 decimal places).
43. Q46A is a 44 matrix with A=2. Two rows of A are interchanged to give B. Find B.
44. Q47A is a 44 matrix with A=2. Find (AT A).
45. Q48A is a 44 matrix with A=-1. Find (-1A).
46. Q49A and B are 22 matrices with A=3 and B=-1. Find (AB).
47. Q50A is an invertible 22 matrix with A=-2. Find (A-1) (2 decimal places).
48. Q51A is a 22 matrix with A=5. Two rows of A are interchanged to give B. Find B.
49. Q52A is a 22 matrix with A=-2. Find (AT A).
50. Q53For which value of k is the matrix (matrix) singular (not invertible)?
51. Q54For which value of k is the matrix (matrix) singular (not invertible)?
52. Q55For which value of k is the matrix (matrix) singular (not invertible)?
53. Q56For which value of k is the matrix (matrix) singular (not invertible)? Select all th…
54. Q57Find the entry in row 1, column 2 of the inverse of A=(matrix) (2 decimal places).
55. Q58Find the entry in row 1, column 1 of the inverse of A=(matrix) (2 decimal places).
56. Q59Find the entry in row 1, column 1 of the inverse of A=(matrix) (2 decimal places).
57. Q60Find the entry in row 1, column 2 of the inverse of A=(matrix) (2 decimal places).
58. Q61Find the entry in row 2, column 2 of the inverse of A=(matrix) (2 decimal places).
59. Q62Find the entry in row 1, column 1 of the inverse of A=(matrix) (2 decimal places).
60. Q63Find the entry in row 1, column 1 of the inverse of A=(matrix) (2 decimal places).
61. Q64Find the entry in row 1, column 2 of the inverse of A=(matrix) (2 decimal places). Select
62. Q65The system Ax=b with A=(matrix) and b=(matrix) has
63. Q66The system Ax=b with A=(matrix) and b=(matrix) has
64. Q67The system Ax=b with A=(matrix) and b=(matrix) has
65. Q68The system Ax=b with A=(matrix) and b=(matrix) has
66. Q69The system Ax=b with A=(matrix) and b=(matrix) has
67. Q70The system Ax=b with A=(matrix) and b=(matrix) has
68. Q71The system Ax=b with A=(matrix) and b=(matrix) has
69. Q72The system Ax=b with A=(matrix) and b=(matrix) has
70. Q73The system Ax=b with A=(matrix) and b=(matrix) has
71. Q74The system Ax=b with A=(matrix) and b=(matrix) has
72. Q75The system Ax=b with A=(matrix) and b=(matrix) has
73. Q76The system Ax=b with A=(matrix) and b=(matrix) has
74. Q77Solve the system 3x + 3y = -6 , 3x - y = -10 and find the value of x+y.
75. Q78Solve the system -y - 2z = -8 , 4x - 3y = -6 , 4x + 4z = 12 and find the value of x+y+z.
76. Q79Solve the system 3x - 2y = -6 , -x + 3y = 9 and find the value of x+y.
77. Q80Solve the system 4x - 3y + z = 25 , -3x + y + 4z = -15 , 4y + 2z = -12 and find the value
78. Q81Solve the system -2x + 2y = 12 , 3x + y = -6 and find the value of x+y.
79. Q82Solve the system 4x + 4y - 3z = 41 , -x - y - 3z = 1 , 3x + 2y + 2z = 14 and find the valu
80. Q83Select all the true statements.
81. Q84Which of the following statements are true?
82. Q85Choose the correct statements about vectors, matrices and determinants.
83. Q86Select every correct statement.
84. Q87Which of these facts about matrices hold?
85. Q88Read each statement and select those that are true.
86. Q89Which statements are correct?
87. Q90Mark all the true statements.
88. Q91The figure shows the vectors u and v in the plane (their end points are marked). Find u v.
89. Q92The figure shows the vectors u and v in the plane (their end points are marked). Find the
90. Q93The figure shows the vectors u and v in the plane (their end points are marked). The angle
91. Q94The figure shows the vectors u and v in the plane (their end points are marked). Find the
92. Q95The figure shows the vectors u and v in the plane (their end points are marked). Find |u|2
93. Q96Refer to the figure. The figure shows the vectors u and v in the plane (their end points a
94. Q97Refer to the figure. The figure shows the vectors u and v in the plane (their end points a
95. Q98Refer to the figure. The figure shows the vectors u and v in the plane (their end points a
96. Q99Refer to the figure. The figure shows the vectors u and v in the plane (their end points a
97. Q100Refer to the figure. The figure shows the vectors u and v in the plane (their end points a