2x2 matrix over complex A^2025=(2025) find A

W subspace of R^4 solution x1+x2-x3-x4=0 find basis for orthogonal complement Wㅗ. find v1 in W v2 in Wㅗ such that v1+v2= (1,1,0,1)

n dim vector space V over C. T:V to V.  such that T^3=T find all possible characteristic polynomial and minimal polynomial. show that V= imT direct sum ker T

show that x^4+x^2+3 is irreducible over F7. prove that frobenius mapping is automorphism. find the number of element a in K such that orbit (a) with 2 element.

R^2-Q^2 path connected

product of two bounded uniformly convergent sequences of functions is convergent

못풀었지만 기억나는것들: R/~ 정수 전부 붙인거 homeo to union of circles (0,n) 중심 반지름 n ?

fixed point exist

D^2 이랑 뭐 attaching 해서 homotopy equivalent 였나

regular surface의 normal vector 랑 tangent vector 로 만들어지는 걸로 locally plane 판단


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총 16문제


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