Please solve parts 65-68 of this problem... Take as much time as you need... linear algebra review Problem IV Let V be a subspace of R4 spanned by three vectors given below. Find thedistance 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).

Answered: Image /qna-images/answer/bb707285-1260-42cb-b0e4-eb1fba979a63.jpg

Answered: 65. (1,0, 1,0), (1,1,1,-1), (1,2,3,0).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please solve parts 65-68 of this problem... Take as much time as you need... linear algebra review

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).

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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