[線代] 關於一個推導中的問題

[skyhigh8988 (Aesthetic)]

這一個證明的過程有一個點不懂


L:R^n --> R^m

with the two bases


E=[u1,,,,,,un]


F=[b1,,,,,,,,bn]


then the reduced row echelon form of (b1,,,,,,,bm | L(u1),......L(un))

is (I|A)

-_____________________________________________________________________

PROOF:

     Let B=(b1,,,,,,,,bm). The matrix (B | L(u1),,,,,,,,,,L(un))

is row equivalent to  B^-1 ( B | L(u1),,,,,,,,,L(un)

我想問的是為什麼前面乘一個B的反矩陣仍然會row euqivalent

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.116.117.15
推 znmkhxrw    :應該是因為B是basis 寫成n by n後的determinant不為0
→ znmkhxrw    :所以B^-1也是
→ skyhigh8988 :謝謝您^_^我懂了