[線代] 線性映射和column space

[mqazz1 (無法顯示)]

let V and W be vector spaces with ordered bases E and F, respectively

if L:V->W is a linear transformation and A is the matrix representing L

relative to E and F, show that

(a) v屬於ker(L) if and only if [V] 屬於 N(A)
                                  E

(b) w屬於L(V) if and only if [w] is in the column space of A
                                F

請問這兩題應該怎麼證呢?

我翻過手上書好像沒看到類似的證明@@

有沒有好心的高手可以指點一下 謝謝!!

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