題目很簡單~但是達案跟我做的不一樣........
題目是這樣的
註(bT 是 b得反置矩証) (Rn 有N個元素)
let m=a(bT) where a and b are two nonzero column vector of (Rn) Please answer the follow question
(A)what is rank(M)? det(M)? and trace(M)?
I think....
if a =[a1] [b1] so Rank(M)=Rank(abT) is N
a2 b2
.. b= ..
.. ..
an bn
but the absolute answer is Rank(M)=1...? Why?
therefore det(M) trace(M) also error...
...............................................................................................
Digit 1 to 9 can be arranded into 3-3 matrices in 9! ways. Find the sum of the
determinant of these matrices.
answer is 0
我目前的做法是
因為定理有一敘述是 det(A +or - B) =det(A) +or -det (B)
因此題目鎖有matric加總變成
45 45 45
[ 45 45 45 ] ---->det()=0
45 45 45
但是有但書 det(A +or - B) =det(A) +or -det (B) =>(不是所有狀況都成立)
這樣做有風險 因為定裡不是絕對?
有其他其他方式? 或者證明可以使用det(A +or - B) =det(A) +or -det (B) ??
感激不盡!!