[線代] 幾題線代
Let R^n be regarded as column vectors.
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1.
(a) Let A ∈R^n*n . Show that if A is symmetric and satisfied Ax · x = 0 for
all x ∈R^n , then A = 0.
http://i.imgur.com/6Zv8zsZ.jpg
請問我這樣證可以嗎？但是沒有用到symmetric
(b) Given an example to show that the assumption “symmetric” in (a) is neces
sary.
2. Let X be the linear subspace of R^2*3 containing all matrices whose columns
add to 0 ∈ R^2. Similarly let Y be the subspace of R^2*3 containing all ma
trices whose rows add to 0 ∈R^3.
(a) What is the dimension of X.
(b) What is the dimension of (X+Y).
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※ 編輯: Aquarkbrain (42.76.167.35), 07/07/2018 00:42:30
推
07/07 08:01,
6年前
, 1F
07/07 08:01, 1F
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