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# 兩個線代證明題

a.

Show that if A is an m by n matrix with m < n

then the homogeneous system of linear equations

AX = 0 has a non-trivial solution.

b.

Prove that if a vector space V can be spanned by a .nite set of vectors v1; : : : ; vn , then any

linearly independent set of vectors in V must be .nite and contains no more than n elements

(You can use (a) if you wish.

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