Maths 2 week 4 important questions

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1. Q4Find the dimension of the span of the vectors (3, 0, 3, 3), (-1, 0, -2, 1), (-1, 2, -1, -2
2. Q5Find the dimension of the span of the vectors (2, 2, 3), (1, -1, 0), (-1, 3, 2) in R3.
3. Q6Find the dimension of the span of the vectors (-2, 0, -1, 0), (-1, 2, 3, -2), (-1, 1, 2, 1
4. Q7Find the dimension of the span of the vectors (1, 1, 0), (-2, -2, 1), (-1, -1, 1) in R3.
5. Q8Find the dimension of the span of the vectors (3, 1, 1, 0), (-1, 1, -1, -1), (3, 0, -1, 0)
6. Q9Find the dimension of the span of the vectors (3, 2, -2), (2, 3, 0), (2, -1, 2) in R3.
7. Q10Find the dimension of the span of the vectors (2, 0, -2, -2), (0, 0, -1, -1), (2, 3, 2, 1)
8. Q11Find the dimension of the span of the vectors (2, 1, -2), (-2, 1, -1), (2, -1, 0) in R3.
9. Q12Find the dimension of the span of the vectors (-1, 0, 2, -2), (-2, -2, -2, -1), (2, 3, 2,
10. Q13Find the dimension of the span of the vectors (3, 0, 1), (1, -1, -2), (4, -1, -1) in R3.
11. Q14Find the dimension of the span of the vectors (1, 1, 2, 0), (-2, 3, 3, -1), (1, 3, 3, 0),
12. Q15In R2 the set (-2, 1), (-4, 2) is
13. Q16In R3 the set (2, 2, -1), (-1, 0, -1), (2, -2, 2) is
14. Q17In R3 the set (1, 3, -1), (3, 1, 3), (4, 4, 2) is
15. Q18In R2 the set (-2, 2), (1, 0) is
16. Q19In R3 the set (-2, 0, 2), (3, 1, 0), (1, 1, 2) is
17. Q20In R3 the set (0, 1, -2), (1, 3, 1), (-2, 1, -1) is
18. Q21In R2 the set (1, 2), (1, 2) is
19. Q22In R3 the set (3, -2, -2), (0, 2, 0), (2, 1, -2) is
20. Q23In R3 the set (2, 2, -2), (-2, 2, 1), (0, 4, -1) is
21. Q24In R2 the set (2, -2), (0, -2) is
22. Q25In R3 the set (2, 0, -2), (-2, 1, 0), (0, 1, -2) is
23. Q26In R3 the set (0, 1, -1), (0, -2, 3), (1, 0, 2) is
24. Q27v_1,,v_2 are linearly independent vectors in R3. How many more vectors must be added to ge
25. Q28v_1,,v_2 are linearly independent vectors in R4. How many more vectors must be added to ge
26. Q29v_1,,v_3 are linearly independent vectors in R4. How many more vectors must be added to ge
27. Q30v_1,,v_3 are linearly independent vectors in R5. How many more vectors must be added to ge
28. Q31The vectors (1, 2, 1), (2, 5, 1) and (3,1,k) form a basis of R3 for every k except one val
29. Q32The vectors (1, 2, 1), (2, 3, 1) and (2,1,k) form a basis of R3 for every k except one val
30. Q33Let =b_1=(1, -1), b_2=(-2, 3) be a basis of R2. Find the coordinate of w=(-11, 15) along b
31. Q34Let =b_1=(3, 2, -2), b_2=(-1, 2, 2), b_3=(0, 2, -2) be a basis of R3. Find the coordinate
32. Q35Let =b_1=(-1, -1), b_2=(1, -1) be a basis of R2. Find the coordinate of w=(0, -8) along b_
33. Q36Let =b_1=(2, 2, 3), b_2=(0, 1, -1), b_3=(0, 0, 1) be a basis of R3. Find the coordinate of
34. Q37Let =b_1=(0, -1), b_2=(3, 0) be a basis of R2. Find the coordinate of w=(-6, -1) along b_1
35. Q38Let =b_1=(-2, -1, 2), b_2=(1, 3, -2), b_3=(2, 0, -2) be a basis of R3. Find the coordinate
36. Q39Let =b_1=(0, -2), b_2=(-1, -2) be a basis of R2. Find the coordinate of w=(1, -2) along b_
37. Q40Let =b_1=(1, -2, -1), b_2=(3, -1, -1), b_3=(-1, 2, 3) be a basis of R3. Find the coordinat
38. Q41Let =b_1=(3, -2), b_2=(1, -2) be a basis of R2. Find the coordinate of w=(6, 0) along b_1
39. Q42Let =b_1=(-2, -2, 2), b_2=(3, 0, 2), b_3=(-2, 1, 3) be a basis of R3. Find the coordinate
40. Q43Let =b_1=(3, 2), b_2=(-2, -1) be a basis of R2. Find the coordinate of w=(12, 8) along b_2
41. Q44Let =b_1=(3, -1, 1), b_2=(3, 1, 1), b_3=(2, -1, 2) be a basis of R3. Find the coordinate o
42. Q45Let =b_1=(0, -1), b_2=(1, 3) be a basis of R2. Find the coordinate of w=(0, -1) along b_2
43. Q46Let =b_1=(2, 0, -1), b_2=(3, -2, 0), b_3=(3, 0, 0) be a basis of R3. Find the coordinate o
44. Q47What is the dimension of x R4: x_1+x_2+x_3+x_4=0?
45. Q48What is the dimension of (x,y,z) R3: x+y+z=0? Select all the true statements about the val
46. Q49What is the dimension of (x,y,z) R3: x=y=z?
47. Q50What is the dimension of (x,y,z,w) R4: x=y and z=w?
48. Q51What is the dimension of (x,y,z) R3: x+y=0 and y+z=0?
49. Q52What is the dimension of (x,y,z) R3: x=0?
50. Q53What is the dimension of (x_1,,x_5) R5: x_1=x_2 and x_3=x_4?
51. Q54What is the dimension of (x,y,z,w) R4: x+y=0,, z+w=0,, x-z=0?
52. Q55What is the dimension of the set of all polynomials of degree at most 4?
53. Q56What is the dimension of the set of all polynomials p of degree at most 3 with p(0)=0?
54. Q57What is the dimension of the space of all 23 matrices?
55. Q58What is the dimension of the space of all symmetric 33 matrices?
56. Q59What is the dimension of the space of 33 matrices with trace 0?
57. Q60What is the dimension of the space of all 22 upper triangular matrices?
58. Q61The dimension of (x,y,z) R3: x+y+z=0 is
59. Q62The dimension of (x,y,z,w) R4: x=y and z=w is
60. Q63The dimension of (x,y,z) R3: x=0 is
61. Q64The dimension of (x,y,z,w) R4: x+y=0,, z+w=0,, x-z=0 is
62. Q65The dimension of the set of all polynomials p of degree at most 3 with p(0)=0 is
63. Q66The dimension of the space of all symmetric 33 matrices is
64. Q67A is a 35 matrix of rank 2. What is the dimension of the null space of A (the solutions of
65. Q68A is a 44 matrix and the null space of A has dimension 1. What is the dimension of the col
66. Q69The rows of a 34 matrix span a space of dimension 2. How many linearly independent columns
67. Q70A is a 56 matrix of rank 1. What is the dimension of the null space of A (the solutions of
68. Q71A is a 46 matrix and the null space of A has dimension 4. What is the dimension of the col
69. Q72The rows of a 66 matrix span a space of dimension 5. How many linearly independent columns
70. Q73The rows of a 34 matrix span a space of dimension 1. How many linearly independent columns
71. Q74A is a 56 matrix of rank 3. What is the dimension of the null space of A (the solutions of
72. Q75Select all the true statements.
73. Q76Which of the following statements about basis and dimension are true?
74. Q77Choose the correct statements.
75. Q78Select every true statement.
76. Q79Which statements hold for a vector space?
77. Q80Mark all the correct statements.
78. Q81Which of these are true?
79. Q82Read each statement and select the true ones.
80. Q83The figure shows a basis b_1,b_2 of R2 and a vector w (end points marked). Write w=c_1b_1+
81. Q84The figure shows a basis b_1,b_2 of R2 and a vector w (end points marked). Write w=c_1b_1+
82. Q85Refer to the figure. The figure shows a basis b_1,b_2 of R2 and a vector w (end points mar
83. Q86The figure shows a basis b_1,b_2 of R2 and a vector w (end points marked). Write w=c_1b_1+
84. Q87Look at the diagram given. The figure shows a basis b_1,b_2 of R2 and a vector w (end poin
85. Q88Refer to the figure. The figure shows a basis b_1,b_2 of R2 and a vector w (end points mar
86. Q89Study the figure carefully. The figure shows a basis b_1,b_2 of R2 and a vector w (end poi
87. Q90Look at the diagram given. The figure shows a basis b_1,b_2 of R2 and a vector w (end poin
88. Q91Use the picture shown. The figure shows a basis b_1,b_2 of R2 and a vector w (end points m
89. Q92Study the figure carefully. The figure shows a basis b_1,b_2 of R2 and a vector w (end poi
90. Q93Let W be the subspace of R3 spanned by (-2, 1, 2), (0, 2, 1), (-2, 5, 4). Find W and enter
91. Q94Let W be the subspace of R3 spanned by (3, 2, 2), (2, 1, 3), (-2, -1, 0), (0, -2, -1). Fin
92. Q95Let W be the subspace of R4 spanned by (3, -2, 0, -2), (-2, 3, 2, -1), (0, -1, 2, -2), (0,
93. Q96Let W be the subspace of R4 spanned by (-1, -2, 3, 1), (-2, 1, 3, 2), (2, 3, -2, 2), (-2,
94. Q97Let W be the subspace of R4 spanned by (1, 0, 2, 1), (0, 2, -1, 2), (1, 4, 0, 5). Find W a
95. Q98The vectors b_1=(2, 0, -1), b_2=(2, 2, -2), b_3=(1, 0, 2) form a basis of R3. If w=(3, 0,
96. Q99The vectors b_1=(3, -1, 2), b_2=(-2, -2, 3), b_3=(-1, 0, -2) form a basis of R3. If w=(-7,
97. Q100The vectors b_1=(2, 0, -1), b_2=(-1, 2, 0), b_3=(-1, 3, 2) form a basis of R3. If w=(0, -1