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Problem IV Let V be a subspace of R4 spanned by three vectors given below. Find the distance from the vector y = (0, 0, 12,0) the subspace V. 61. (1,1,1,1), (0,3,2,3), (-3, 5, 1, 1). 62. (1,1,1,1), (1,0,3,0), (1,0,5,-2). 63. (1,1,0,0), (2,0,1,1), (1, -5,2,0). 64. (1,0, 1, 1), (1,1,2,0), (0, 1, 4,2). 65. (1,0, 1,0), (1,1,1,-1), (1,2,3,0). 66. (1,0,0,1), (0,1,1,-2), (1,-1,3,3). 67. (1,1,-1,1), (2,3,0,3), (1, 1, 3, 5). 68. (1,0,0,-1), (2,1,1,0), (1,0, 2,5). 69. (1,0, 1,0), (1,-1, 1,-1), (1,0,3,-2). 70. (1,1,1,-1), (1,3,0,0), (1,5, 0, 2). 71. (1,1,1,1), (2,3,0,3), (1,1, -3,5). 72. (1,1,1,1), (1,3,0,0), (1,5, 0, -2). 73. (1,0,0,1), (2, 1, 1.0), (1,0,2,-5). 74. (1,1,1,0), (1,0, 2, 1), (0, 2, 4, 1). 75. (1,0,1,0), (1,-1, 1, 1), (1,0,3,2). 76. (1,0,1,0), (0, 1, -2, 1), (1,-1, 3, 3). 77. (1,1,1,-1), (2,3,3,0), (1,1,5, 3). 78. (1,0,-1,0), (2,1,0,1), (1,0, 5, 2). 79. (1,0,0,1), (1,-1,-1, 1), (1, 0, -2, 3). 80. (1,1,-1, 1), (1,3,0,0), (1,5, -2,0).

Problem IV Let V be a subspace of R4 spanned by three vectors given below. Find the distance from the vector y = (0, 0, 12,0) the subspace V. 61. (1,1,1,1), (0,3,2,3), (-3, 5, 1, 1). 62. (1,1,1,1), (1,0,3,0), (1,0,5,-2). 63. (1,1,0,0), (2,0,1,1), (1, -5,2,0). 64. (1,0, 1, 1), (1,1,2,0), (0, 1, 4,2). 65. (1,0, 1,0), (1,1,1,-1), (1,2,3,0). 66. (1,0,0,1), (0,1,1,-2), (1,-1,3,3). 67. (1,1,-1,1), (2,3,0,3), (1, 1, 3, 5). 68. (1,0,0,-1), (2,1,1,0), (1,0, 2,5). 69. (1,0, 1,0), (1,-1, 1,-1), (1,0,3,-2). 70. (1,1,1,-1), (1,3,0,0), (1,5, 0, 2). 71. (1,1,1,1), (2,3,0,3), (1,1, -3,5). 72. (1,1,1,1), (1,3,0,0), (1,5, 0, -2). 73. (1,0,0,1), (2, 1, 1.0), (1,0,2,-5). 74. (1,1,1,0), (1,0, 2, 1), (0, 2, 4, 1). 75. (1,0,1,0), (1,-1, 1, 1), (1,0,3,2). 76. (1,0,1,0), (0, 1, -2, 1), (1,-1, 3, 3). 77. (1,1,1,-1), (2,3,3,0), (1,1,5, 3). 78. (1,0,-1,0), (2,1,0,1), (1,0, 5, 2). 79. (1,0,0,1), (1,-1,-1, 1), (1, 0, -2, 3). 80. (1,1,-1, 1), (1,3,0,0), (1,5, -2,0).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please work out and explain Parts 76-80. Thank you
Problem IV Let V be a subspace of R4 spanned by three vectors given below. Find the distance from the vector y = (0, 0, 12, 0) the subspace V. 61. (1,1, 1, 1), (0,3,2,3), (-3, 5, 1, 1). 62. (1,1, 1, 1), (1,0,3,0), (1, 0,5, -2). 63. (1,1,0,0), (2,0,1,1), (1, -5,2,0). 64. (1,0, 1, 1), (1, 1,2,0), (0, 1, 4, 2). 65. (1,0,1,0), (1, 1, 1,-1), (1,2,3,0). 66. (1,0,0,1), (0, 1, 1,-2), (1,-1,3,3). 67. (1,1,-1, 1), (2,3,0,3), (1, 1, 3, 5). 68. (1,0,0,-1), (2,1,1,0), (1,0, 2, 5). 69. (1,0, 1,0), (1,-1, 1,-1), (1, 0, 3, -2). 70. (1,1,1,-1), (1,3,0,0), (1,5, 0, 2). 71. (1,1,1, 1), (2,3,0,3), (1, 1, -3,5). 72. (1, 1, 1, 1), (1,3,0,0), (1,5, 0, -2). 73. (1,0,0,1), (2, 1, 1,0), (1,0,2,-5). 74. (1,1,1,0), (1, 0, 2, 1), (0, 2, 4, 1). 75. (1,0,1,0), (1,-1, 1, 1), (1,0,3, 2). 76. (1,0,1,0), (0, 1, -2, 1), (1,-1,3,3). 77. (1,1,1,-1), (2,3,3,0), (1,1,5,3). 78. (1,0,-1,0), (2, 1, 0, 1), (1,0,5, 2). 79. (1,0,0,1), (1,-1,-1, 1), (1, 0, -2, 3). 80. (1,1,-1,1), (1,3,0,0), (1,5, -2,0).
Transcribed Image Text:Problem IV Let V be a subspace of R4 spanned by three vectors given below. Find the distance from the vector y = (0, 0, 12, 0) the subspace V. 61. (1,1, 1, 1), (0,3,2,3), (-3, 5, 1, 1). 62. (1,1, 1, 1), (1,0,3,0), (1, 0,5, -2). 63. (1,1,0,0), (2,0,1,1), (1, -5,2,0). 64. (1,0, 1, 1), (1, 1,2,0), (0, 1, 4, 2). 65. (1,0,1,0), (1, 1, 1,-1), (1,2,3,0). 66. (1,0,0,1), (0, 1, 1,-2), (1,-1,3,3). 67. (1,1,-1, 1), (2,3,0,3), (1, 1, 3, 5). 68. (1,0,0,-1), (2,1,1,0), (1,0, 2, 5). 69. (1,0, 1,0), (1,-1, 1,-1), (1, 0, 3, -2). 70. (1,1,1,-1), (1,3,0,0), (1,5, 0, 2). 71. (1,1,1, 1), (2,3,0,3), (1, 1, -3,5). 72. (1, 1, 1, 1), (1,3,0,0), (1,5, 0, -2). 73. (1,0,0,1), (2, 1, 1,0), (1,0,2,-5). 74. (1,1,1,0), (1, 0, 2, 1), (0, 2, 4, 1). 75. (1,0,1,0), (1,-1, 1, 1), (1,0,3, 2). 76. (1,0,1,0), (0, 1, -2, 1), (1,-1,3,3). 77. (1,1,1,-1), (2,3,3,0), (1,1,5,3). 78. (1,0,-1,0), (2, 1, 0, 1), (1,0,5, 2). 79. (1,0,0,1), (1,-1,-1, 1), (1, 0, -2, 3). 80. (1,1,-1,1), (1,3,0,0), (1,5, -2,0).
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