2. For each of the following homogeneous systems of linear equations, fin the dimension of and a basis for the solution space. (a) x1+3x2 = 0 x1 + x2 - (b) x3 = 0 2x1 + 6x2 = 0 4x1+x22x3 = 0 (c) x12x2 - x3 = 0 2x1 + x2 - x3=0 2x1 + x2 (d) - x3 = 0 x1- x2 x3=0 x12x22x3 = 0
2. For each of the following homogeneous systems of linear equations, fin the dimension of and a basis for the solution space. (a) x1+3x2 = 0 x1 + x2 - (b) x3 = 0 2x1 + 6x2 = 0 4x1+x22x3 = 0 (c) x12x2 - x3 = 0 2x1 + x2 - x3=0 2x1 + x2 (d) - x3 = 0 x1- x2 x3=0 x12x22x3 = 0
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Section 3.3: 2(d)only!
Transcribed Image Text:2. For each of the following homogeneous systems of linear equations, find
the dimension of and a basis for the solution space.
(a)
x1 + 3x2 = 0
(b)
2x1 + 6x2 = 0
x1 + x2 x3 = 0
4x1+x22x3 = 0
-
2x1 + x2
x3=0
x12x2
-
x3 = 0
(c)
(d)
-
x1- x2
x3 = 0
2x1 + x2
x3 = 0
x12x22x3 = 0
-
(e) x12x2 3x3 + x4 = 0
(f)
x1+ 2x2 = 0
x1
-
x2 = 0
x12x2
(g)
x3 + x4 = 0
x2
x3 + x4 = 0
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