[理工] [線代]交大100
9.Suppose A:3x3 has three distinct eigenvalues 0,1,3 with corresponding
eigenvectors u,v,w. 何者敘述正確
A.The rank of A must be 2
B.The matrix A^2-I is invertible
C.v and w must span the column space of A
D.The least squares error of Ax=2v+3w+u must be ∥u∥^2
10.Suppose A:3x3 = xy^T is rank 1 matrix.何者敘述正確
A.The eigenvector matrix S must be invertible
B.A must have one non-zero eigenvalue
C.When A is facotrized by SVD into UΣV^T,the only non-zero singular value
is ∥x∥∥y∥
D.When A is factorized by SVD into UΣV^T,U must include x/∥x∥ as
one of its column vectors
請問這兩題要怎麼選 腦袋轉不過來
覺得觀念考好多orz
順便再問幾個選項
1. A,B,A+B,都是n*n可逆矩陣, then A^-1 +B^-1 也可逆
我是選FALSE 總覺得舉得出反例 不過想不到
┌ ┐
2.If │a b c│
det│d e f│=7
│1 3 5│
└ ┘
第三列改1 0 1的時候 det為9, then 第三列改1 6 9的時候=5
(排版麻煩 我用文字敘述)
true or false?
我對題目給的兩種展開 然後把三種coefficient用變數A B C代換
但這樣也只有兩條方程式 三個未知數解不出來 有別的辦法嗎?
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◆ From: 111.250.214.190
※ 編輯: death888 來自: 111.250.214.190 (02/19 00:35)
推
02/19 00:49, , 1F
02/19 00:49, 1F
→
02/19 00:50, , 2F
02/19 00:50, 2F
→
02/19 00:50, , 3F
02/19 00:50, 3F
推
02/19 06:08, , 4F
02/19 06:08, 4F
推
02/19 14:04, , 5F
02/19 14:04, 5F
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