Determine the dimension of and a basis for the solution space of the homogeneous linear system. 3x1 +x2 +3x3 = 0 X1 +7x3 = 0 X2 +x3 = 0 [0, 0, 1]". O The dimension of the solution space is 3, the basis is v1 = [1, 0, 0j', v2 = [0, 1, 0]', v3 = O The dimension of the solution space is zero, the basis is the empty set. O The dimension of the solution space is 2, the basis is vi = [1,0, 3]", v2 = [0, 1, 7]". O The dimension of the solution space is 3, the basis is v1 = [1,0, 3]', V2 = [0, 1, 7]', v3 = [0, 0, 1]'. O 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 +3x3 = 0 X1 +7x3 = 0 X2 +x3 = 0 [0, 0, 1]". O The dimension of the solution space is 3, the basis is v1 = [1, 0, 0j', v2 = [0, 1, 0]', v3 = O The dimension of the solution space is zero, the basis is the empty set. O The dimension of the solution space is 2, the basis is vi = [1,0, 3]", v2 = [0, 1, 7]". O The dimension of the solution space is 3, the basis is v1 = [1,0, 3]', V2 = [0, 1, 7]', v3 = [0, 0, 1]'. O 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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Question
9
![Determine the dimension of and a basis for the solution space of the homogeneous linear system.
3x1 +x2 +3x3
= 0
X1
+7x3
= 0
X2
+x3
= 0
O The dimension of the solution space is 3, the basis is v1 = [1,0, 0]", v2 = [0, 1, 0], v3 = [0, 0, 1]'.
O The dimension of the solution space is zero, the basis is the empty set.
O The dimension of the solution space is 2, the basis is v1 = [1,0, 3]', v2 = [0, 1, 7]'.
O The dimension of the solution space is 3, the basis is vị = [1, 0, 3]', V2 = [0, 1, 7]', v3 = [0, 0, 1]'.
O The dimension of the solution space is 2, the basis is v1 = [1,0, 7]', v2 = [0, 1, 3]'.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b7f52fc-6519-4f50-afed-473b8fbf53c1%2Fe20f5fe0-a95f-4bc1-bd32-2e16ef3f8510%2F6dp10ah_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 +3x3
= 0
X1
+7x3
= 0
X2
+x3
= 0
O The dimension of the solution space is 3, the basis is v1 = [1,0, 0]", v2 = [0, 1, 0], v3 = [0, 0, 1]'.
O The dimension of the solution space is zero, the basis is the empty set.
O The dimension of the solution space is 2, the basis is v1 = [1,0, 3]', v2 = [0, 1, 7]'.
O The dimension of the solution space is 3, the basis is vị = [1, 0, 3]', V2 = [0, 1, 7]', v3 = [0, 0, 1]'.
O The dimension of the solution space is 2, the basis is v1 = [1,0, 7]', v2 = [0, 1, 3]'.
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