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**Unformatted text preview: **Ax = b is obtained by translating the solution set of Ax = 0. • ( T / F ) The columns of the matrix A are linearly independent if the equation Ax = 0 has the trivial solution. • ( T / F ) If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S . • ( T / F ) Let A and B be m × n matrices. If A is row-equivalent to B , then Col ( A ) = Col ( B ). ( Col ( A ) is the column space of A .) • ( T / F ) The vectors running from the origin to the plane deﬁned by the equation x + 2 y + 3 z = 0 form a subspace of R 4 . • ( T / F ) If addition is redeﬁned as a ⊕ b = a + 2 b , then R 2 using this new addition is not a vector space. 1 TA: Kyle Wilson...

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