Determine the dimension of and a basis for the solution space of the homogeneous linear system. 3x₁ + x₂ +9x3 = 0 XI +7x3 = 0 X2₂ +x3 = 0 O The dimension of the solution space is 2, the basis is V₁ = [1,0, 3], V₂ = [0, 1, 7]¹. The dimension of the solution space is 3, the basis is V₁ = [1, 0, 0], v₂ = [0, 1, 0]", V3 = = [0, 0, 1]¹. The dimension of the solution space is zero, the basis is the empty set. = The dimension of the solution space is 3, the basis is V₁ [1, 0, 3], V₂ = [0, 1, 7], V3 = [0, 0, 1]. The dimension of the solution space is 2, the basis is V₁ = [1, 0, 7]", v₂ = [0, 1, 3]".
Determine the dimension of and a basis for the solution space of the homogeneous linear system. 3x₁ + x₂ +9x3 = 0 XI +7x3 = 0 X2₂ +x3 = 0 O The dimension of the solution space is 2, the basis is V₁ = [1,0, 3], V₂ = [0, 1, 7]¹. The dimension of the solution space is 3, the basis is V₁ = [1, 0, 0], v₂ = [0, 1, 0]", V3 = = [0, 0, 1]¹. The dimension of the solution space is zero, the basis is the empty set. = The dimension of the solution space is 3, the basis is V₁ [1, 0, 3], V₂ = [0, 1, 7], V3 = [0, 0, 1]. The dimension of the solution space is 2, the basis is V₁ = [1, 0, 7]", v₂ = [0, 1, 3]".
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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![Determine the dimension of and a basis for the solution space of the homogeneous linear system.
3x₁ + x₂ +9x3
= 0
= 0
XI
+7x3
x2
+x3
= 0
The dimension of the solution space is 2, the basis is V₁ = [1, 0, 3]", V₂ = [0, 1, 7]¹.
The dimension of the solution space is 3, the basis is V₁ = [1, 0, 0], V₂ = [0, 1, 0], V3 = [0, 0, 1]¹.
O The dimension of the solution space is zero, the basis is the empty set.
The dimension of the solution space is 3, the basis is V₁ = [1, 0, 3], V₂ =
The dimension of the solution space is 2, the basis is V₁ = [1, 0, 7]¹, V₂ =
[0, 1, 7], V3 = [0, 0, 1]¹.
[0, 1,3].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa81fdab9-44ee-4722-8209-0f0fd1748547%2F37160de8-34ef-48a8-845e-037bb48854f7%2Fkfv4cp4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine the dimension of and a basis for the solution space of the homogeneous linear system.
3x₁ + x₂ +9x3
= 0
= 0
XI
+7x3
x2
+x3
= 0
The dimension of the solution space is 2, the basis is V₁ = [1, 0, 3]", V₂ = [0, 1, 7]¹.
The dimension of the solution space is 3, the basis is V₁ = [1, 0, 0], V₂ = [0, 1, 0], V3 = [0, 0, 1]¹.
O The dimension of the solution space is zero, the basis is the empty set.
The dimension of the solution space is 3, the basis is V₁ = [1, 0, 3], V₂ =
The dimension of the solution space is 2, the basis is V₁ = [1, 0, 7]¹, V₂ =
[0, 1, 7], V3 = [0, 0, 1]¹.
[0, 1,3].
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