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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
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 +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]'.
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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