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Math  /  Algebra

QuestionWhich of the following sets are subspaces of R3\mathbb{R}^{3} ? A. {(x,y,z)∣−5x−2y+4z=−8}\{(x, y, z) \mid-5 x-2 y+4 z=-8\} B. {(8x,5x,2x)∣x\{(8 x, 5 x, 2 x) \mid x arbitrary number }\} C. {(x,y,z)∣9x−3y=0,6x+8z=0}\{(x, y, z) \mid 9 x-3 y=0,6 x+8 z=0\} D. {(−9,y,z)∣y,z\{(-9, y, z) \mid y, z arbitrary numbers }\} E. {(x,y,z)∣x,y,z>0}\{(x, y, z) \mid x, y, z>0\} F. {(x,y,z)∣x+y+z=0}\{(x, y, z) \mid x+y+z=0\}

Studdy Solution
Sets B, C, and F satisfy all three conditions for being subspaces of R3\mathbb{R}^3.
The sets that are subspaces of R3\mathbb{R}^3 are:
B, C, F \text{B, C, F}

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