Answers to Quizlet 2.9

1. If the null space of an 8 by 5 matrix is two-dimensional, what is the dimension of the column space of the matrix?

Answer: number of columns=dim(null space)+ dim(column space) so the answer is 3.

2. Consider the set of points (x,y,z) in R^3. Is the set of points satisfying x+y+z=1 a subspace of R^3?

Answer: No, (0,0,0) is not in the set of points satisfying x+y+z=1.

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