Re: [理工] 線代
看板Grad-ProbAsk作者Murasaki0110 (Paradise Lost)時間13年前 (2012/10/20 20:45)推噓5(5推 0噓 16→)留言21則, 7人參與討論串37/120 (看更多)
: (5)Let A be an n by n matrix with characteristic polynomial
: f(t). Let g(t) be a polynomiql for which 0<deg(g(t))<deg(f(t)).
: Then, g(A)=/=0.
: F:這題在考什麼?
他說給你一個比f(t)次方低的多項式，代A進去都不等於0，但顯然不是這樣
: (6)Consider a n*nreal-valued matrix A. Wich of the following
: statements are equivalent to "A is nonsingular"
: (a)The system of n linear equations in n unknowns Ax=e1
: has a unique solution,where e1=(1,0,...,0)^T.
: (b)A^2+3A+I is nonsingular.
: (c)A^2+4A
: Ans:a
: (c)我用det(A^2+4A)=det(A(A+4I)=det(A)det(A+4I)=\=0
: =>det(A)=/=0,det(A+4I)=\=0 => A is nonsingular.
: 這樣c不也對嗎?
: 還有a,b要怎判斷?
你這個證法導果為因了，det(A)有可能是0
: (7)If S generates the vector space V,then every vector in V can
: be written as a linear combination of elements of S in only
: one way.
: T:是因為題目說"S generates the vector space V",才得到span(S)
: 是V的一組基底嗎?
我覺得是F耶，因為S中的vectors不一定獨立
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