Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for the dimension and in any cell of the vector.) X₁ + 2x₂-3x3-11x4 + 8x5 = 0 X₁ + 3x3 + x4 + 6x5 = 0 2x₁ + 6x₂ - 12x3 - 34x4 + 18x5 = 0 1 X dimension basis -2311 106 0-20 010 001
Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for the dimension and in any cell of the vector.) X₁ + 2x₂-3x3-11x4 + 8x5 = 0 X₁ + 3x3 + x4 + 6x5 = 0 2x₁ + 6x₂ - 12x3 - 34x4 + 18x5 = 0 1 X dimension basis -2311 106 0-20 010 001
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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please answer this question
![Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for the dimension and in any cell of the vector.)
X₁ + 2x₂ − 3x3 - 11x4 + 8x5 = 0
X₁ + 3x3 + x4 + 6x5
= 0
2x₁ + 6x₂ - 12x3 34x4 + 18x5
= 0
1
1
X
dimension
basis
X
-2311
106
0-20
010
001
-
↓ ↑
A basis for a solution space consists of linearly independent vectors that span the space. The dimension of the solution space is determined by the number of vectors in the basis. One way to obtain
possible vectors is by solving an augmented matrix. What is the augmented matrix for this system of equations? How can a solution be obtained from the augmented matrix?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2903bb2a-771d-40b7-a62d-703de2e08baa%2F11a2aeb7-2cc4-414a-be54-13d2b0b5b358%2Fid1k1km_processed.png&w=3840&q=75)
Transcribed Image Text:Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for the dimension and in any cell of the vector.)
X₁ + 2x₂ − 3x3 - 11x4 + 8x5 = 0
X₁ + 3x3 + x4 + 6x5
= 0
2x₁ + 6x₂ - 12x3 34x4 + 18x5
= 0
1
1
X
dimension
basis
X
-2311
106
0-20
010
001
-
↓ ↑
A basis for a solution space consists of linearly independent vectors that span the space. The dimension of the solution space is determined by the number of vectors in the basis. One way to obtain
possible vectors is by solving an augmented matrix. What is the augmented matrix for this system of equations? How can a solution be obtained from the augmented matrix?
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