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).

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

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 42CR: Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a...

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Question

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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