[理工] [線代]線性映射

[dkcheng (電磁霸主)]

                 2   3
 Suppose that T:R →R  is defined by


                       [ 3a-4b ]
              [ a ]    |       |
           T (|   |) = | -a+2b |
              [ b ]    |       |
                       [  5a   ]


determine a spanning set for the null space of T.


答案是 a basis of N(T) is {ψ}


爲什麼會是空集合呢 ?



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推 gskman:令5a=0=>a=0 可得b=0,所以N(T)is{ψ}
推 mp8113f:a、b解得為0 但零向量無法當Basis 定義空集合ψ
推 wsx02:a=b=0
→ dkcheng:ok  剛剛洗澡的時候想到了...感謝
→ feabries:另一種想法是rank(T) = 2 = dim(R^2) 所以nullity(T) = 0
→ feabries:還有要表式空集合用ψ比較洽當吧@@