Find a basis for the solution space of the following homogeneous system of linear equations. 3x1 + 9x2 + 30x3 + 21x4 = 0 5x4 = 0 16x4 = 0 X1 - 3x2 - 8x3 + 2x1 + 12x2 + 38x3 + O {(1, 0, 1, 6), (0, 3, 9, 0), (1, 0, 0, 1)} O {(0, 0, 1, 6), (1, 3, 9, 1)} {(1, 0, 0, 0), (0, 3, 0, 0), (0, 0, 10, 7)} O {(-1, -3, 1, 0), (-18, -1, 0, 3)} O {(1, 0, 0, 0), (0, 3, 0, 0), (0, 0, 10, 0), (0, 0, 0, 7)}

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Find a basis for the solution space of the following homogeneous system of linear equations.
3x1 +
9x2 + 30x3 + 21x4 = 0
x1 -
3x2 -
8x3 +
5x4 = 0
2x₁ + 12x2 + 38x3 + 16x4
= 0
○ {(1, 0, 1, 6), (0, 3, 9, 0), (1, 0, 0, 1)}
O {(0, 0, 1, 6), (1, 3, 9, 1)}
{(1, 0, 0, 0), (0, 3, 0, 0), (0, 0, 10, 7)}
O {(-1, -3, 1, 0), (-18, -1, 0,3)}
O {(1, 0, 0, 0), (0, 3, 0, 0), (0, 0, 10, 0), (0, 0, 0, 7)}
Transcribed Image Text:Find a basis for the solution space of the following homogeneous system of linear equations. 3x1 + 9x2 + 30x3 + 21x4 = 0 x1 - 3x2 - 8x3 + 5x4 = 0 2x₁ + 12x2 + 38x3 + 16x4 = 0 ○ {(1, 0, 1, 6), (0, 3, 9, 0), (1, 0, 0, 1)} O {(0, 0, 1, 6), (1, 3, 9, 1)} {(1, 0, 0, 0), (0, 3, 0, 0), (0, 0, 10, 7)} O {(-1, -3, 1, 0), (-18, -1, 0,3)} O {(1, 0, 0, 0), (0, 3, 0, 0), (0, 0, 10, 0), (0, 0, 0, 7)}
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