※ 引述《thank1984 (thankakimo)》之铭言： : 是非题: : a) Every vector space that is spanned by a finite set has a basis : True : b) Every subspace of a finite-dimensional space is finite-dimensional : False 设V为finite-dimensional space S为其subspace => S包含於V => 0≦dim(S)≦dim(V) => S is finite-dimensional 所以本题为true : c) The only entries of an elementary matrix are zeros and ones : True (3) R 为elementary matrix，但其元素不全为0或1 12 补充：an elementary matrix有3种 (k) (k) (1)R (2)R (3)R 其中k€F ij i ij 本题为False : d) The sum of two n*n elementary matrices is an elementray matrix. : False : e) Every finite-dimensional inner product space posseses an : orthornormal basis. : False Every finite-dimensional inner product space的basis 皆可利用Gram-Schmidt orthogonal process得到一组orthornormal basis 本题为true : 以上是非题答案小弟都不太确定 所以请大大们帮小弟检查一下是否有写错 : 麻烦各位大大了 感谢 有错麻烦各位帮忙订正 --

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