etermine the dimension of and a basis for the solution space of the homogeneous linear system. 3x1 +x2 +3xZ = 0 +6x3 = 0 x2 +x3 = 0 O The dimension of the solution space is 3, the basis is vi = [1,0, 3]", v2 = [0, 1, 6]", 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, 6]". O The dimension of the solution space is 3, the basis is v1 = [1, 0, 01", v2 = [0, 1, 0]", V3 = [0, 0, 1]". O The dimension of the solution space is 2, the basis is v1 = [1, 0, 6]°, v2 = [0, 1, 3]".

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Determine the dimension of and a basis for the solution space of the homogeneous linear system.
3x1 +x2 +3x3
= 0
+6x3
= 0
X2
+x3
O The dimension of the solution space is 3, the basis is vi = [1, 0, 3]°, v2 = [0, 1, 6]",
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, 6]".
O The dimension of the solution space is 3, the basis is v1 = [1,0, 0]², v2 =
V3 = [0, 0, 1]".
O The dimension of the solution space is 2, the basis is v1 = [1, 0, 6]', v2 =
[0, 1, 01",
[О, 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 +6x3 = 0 X2 +x3 O The dimension of the solution space is 3, the basis is vi = [1, 0, 3]°, v2 = [0, 1, 6]", 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, 6]". O The dimension of the solution space is 3, the basis is v1 = [1,0, 0]², v2 = V3 = [0, 0, 1]". O The dimension of the solution space is 2, the basis is v1 = [1, 0, 6]', v2 = [0, 1, 01", [О, 1, 3]".
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