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Question 2
Consider the following system of homogeneous linear equations:
$x_1 - 3x_2 - 9x_3 - 5x_4 = 0$
$2x_1 + x_2 - 4x_3 + 11x_4 = 0$
$x_1 + 3x_2 + 3x_3 + 13x_4 = 0$
Then:
a. The solution space is spanned by \{(3, -2, 1, 0), (4, -3, 0, 1)\}, and has dimension 4.
b. The solution space is spanned by \{(3, 2, 1, 0), (-4, -3, 0, 1)\}, and has dimension 4.
c. The solution space is spanned by \{(3, -2, 1, 0), (4, -3, 0, 1)\}, and has dimension 2.
d. The solution space is spanned by \{(3, -2, 1, 0), (-4, 3, 0, 1)\}, and has dimension 4.
e. The solution space is spanned by \{(3, -2, 1, 0), (-4, 3, 0, 1)\}, and has dimension 2.
f. The solution space is spanned by \{(3, -2, 1, 0), (-4, -3, 0, 1)\}, and has dimension 2.