Andy 發問時間: 科學數學 · 3 年前

線性代數vector spaces的問題!求救!?

Let v1=(1,0,1),v2=(2,1,3),v3=(4,2,6), and w=(3,1,2).

a. Is w in {v1, v2, v3}? How many vectors are in {v1, v2, v3}?

b. How many vectors are in Span{v1, v2, v3}?

c. Is w in the subspace spanned by {v1, v2, v3}? Why?

請問這問題該怎麼解

解答上說明是

a.There are only three vectors in {v1, v2, v3}, and w is not one of them.

b. There are infinitely many vectors in Span{v1, v2, v3}.

c. w is in Span {v1, v2, v3}.

但是小弟我實在是看不懂

請教各位數學高手ˊˋ

2 個解答

評分
  • 3 年前
    最佳解答

    a. {v1, v2, v3}, 大括號的集合表示法, 此集合只有三個元素: v1=(1,0,1),v2=(2,1,3),and v3=(4,2,6). Obviously w=(3,1,2) is not there.

    b./c. Span{v1, v2, v3} = {all linear combinations of v1,v2, and v3}={(u1,u2,u3) | (u1, u2, u3)=c1v1+c2v2+c3v3, for some c1,c2,c3 constants}. Therefore w is in Span{v1, v2, v3}.

    閣下的問題在數學符號的誤解

  • 3 年前

    我大概知道您意思了,謝謝解答!

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