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  1. A = [1, 0; 0, 0; 0, 1; 0, 0];
  2. B = basis3_2b(A)
  3.  
  4. ans =
  5.  
  6. a basis for Col A is
  7.  
  8.  
  9.  
  10. B =
  11.  
  12. 1 0
  13. 0 0
  14. 0 1
  15. 0 0
  16.  
  17. a basis for R^4 is
  18.  
  19. B =
  20.  
  21. 1 0 0 0
  22. 0 0 -1 0
  23. 0 1 0 0
  24. 0 0 0 1
  25.  
  26.  
  27. B =
  28.  
  29. 1 0 0 0
  30. 0 0 -1 0
  31. 0 1 0 0
  32. 0 0 0 1
  33.  
  34. A = [2, 0; 4, 0; 1, 0; 0, 0];
  35. B = basis3_2b(A)
  36.  
  37. ans =
  38.  
  39. a basis for Col A is
  40.  
  41.  
  42.  
  43. B =
  44.  
  45. 2
  46. 4
  47. 1
  48. 0
  49.  
  50. a basis for R^4 is
  51.  
  52. B =
  53.  
  54. 2.0000 -0.8729 -0.2182 0
  55. 4.0000 0.4696 -0.1326 0
  56. 1.0000 -0.1326 0.9668 0
  57. 0 0 0 1.0000
  58.  
  59.  
  60. B =
  61.  
  62. 2.0000 -0.8729 -0.2182 0
  63. 4.0000 0.4696 -0.1326 0
  64. 1.0000 -0.1326 0.9668 0
  65. 0 0 0 1.0000
  66.  
  67. A = magic(3)
  68.  
  69. A =
  70.  
  71. 8 1 6
  72. 3 5 7
  73. 4 9 2
  74.  
  75. B = basis3_2b(A)
  76.  
  77. ans =
  78.  
  79. a basis for Col A is
  80.  
  81.  
  82.  
  83. B =
  84.  
  85. 8 1 6
  86. 3 5 7
  87. 4 9 2
  88.  
  89. a basis for R^3 is
  90.  
  91. B =
  92.  
  93. 8 1 6
  94. 3 5 7
  95. 4 9 2
  96.  
  97.  
  98. B =
  99.  
  100. 8 1 6
  101. 3 5 7
  102. 4 9 2
  103.  
  104. A = magic(6)
  105.  
  106. A =
  107.  
  108. 35 1 6 26 19 24
  109. 3 32 7 21 23 25
  110. 31 9 2 22 27 20
  111. 8 28 33 17 10 15
  112. 30 5 34 12 14 16
  113. 4 36 29 13 18 11
  114.  
  115. B = basis3_2b(A)
  116.  
  117. ans =
  118.  
  119. a basis for Col A is
  120.  
  121.  
  122.  
  123. B =
  124.  
  125. 35 1 6 26 19
  126. 3 32 7 21 23
  127. 31 9 2 22 27
  128. 8 28 33 17 10
  129. 30 5 34 12 14
  130. 4 36 29 13 18
  131.  
  132. a basis for R^6 is
  133.  
  134. B =
  135.  
  136. 35.0000 1.0000 6.0000 26.0000 19.0000 0.5000
  137. 3.0000 32.0000 7.0000 21.0000 23.0000 0.0000
  138. 31.0000 9.0000 2.0000 22.0000 27.0000 -0.5000
  139. 8.0000 28.0000 33.0000 17.0000 10.0000 -0.5000
  140. 30.0000 5.0000 34.0000 12.0000 14.0000 0.0000
  141. 4.0000 36.0000 29.0000 13.0000 18.0000 0.5000
  142.  
  143.  
  144. B =
  145.  
  146. 35.0000 1.0000 6.0000 26.0000 19.0000 0.5000
  147. 3.0000 32.0000 7.0000 21.0000 23.0000 0.0000
  148. 31.0000 9.0000 2.0000 22.0000 27.0000 -0.5000
  149. 8.0000 28.0000 33.0000 17.0000 10.0000 -0.5000
  150. 30.0000 5.0000 34.0000 12.0000 14.0000 0.0000
  151. 4.0000 36.0000 29.0000 13.0000 18.0000 0.5000
  152.  
  153. diary off
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