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< Ostalo ~ inštr/pomoč pri nalogi za podipl študentko na izmenjavi ASAP |
| anah |
 Objavljeno: 29 Okt 2010 17:54 |
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Pridružen/-a: 29.10. 2010, 17:31
Prispevkov: 2
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Zdravo.
Če kdo zna rešiti spodnje naloge, prosim, naj kontaktira Aleno. Je študentka na podiplomski izmenjavi in potrebuje pomoč pri reševanju naloge. Nekaj preoblemov je rešila sama, vendar bi rada preverila z nekom, ki stvar obvlada in ji lahko razloži/potrdi, potek reševanja. Poleg rešitev torej potrebuje tudi konzultacije (inštrukcije).
Za kar je seveda pripravljena plačati, to se dogovorite z njo po mailu.
Sama ji ne znam pomagati, ker so mi ti problemi pretežki. Ker pa ne govori slovensko, sem se odločila, da ji pomagam , se registriram in objavim sporočilo na vašem forumu. Torej, če govoriš angleško in znaš rešiti naloge, prosim kontaktiraj aleno na njen email alena_ist@yahoo.com
Pomoč potrebuje čimprej, rok za oddajo ima že 4.11.2010. |
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| anah |
| Objavljeno: 29 Okt 2010 17:55 |
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Pridružen/-a: 29.10. 2010, 17:31
Prispevkov: 2
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Aja, še naloge - so iz Linearne algebre:
1. Determine a, b and c, such that the solution set of the system
x + 3y + z = 2
4x + ay + bz = c
2x + 7y + 3z = 0
(a) contains infinitely many solutions,
(b) contains exactly one solution,
(c) is empty.
Give separate answers for each part and justify them.
2. For each of the following
{[
]
}
a
(a) A =
; a ∈ R ⊆ R2
a+2
a
b ; a + b = 0, 2a − b + c = 0 ⊆ R3
(b) B =
c
{
}
(c) C = A ∈ Rn×n ; A = AT
{[
]
}
a 1
(d) D =
;a ∈ R
0 a
answer (and argue) the questions:
• Is the set a vector space?
• If YES, find a basis and dimension.
3. Let W1 and W2 be two linear subspaces of a vector space V . Prove that their intersection
W1 ∩ W2 = {v ∈ V ; v ∈ W1 , v ∈ W2 }
is also a vector space.
4. Let
2
4 −2 1
A = −2 −5 7 3
3
7 −8 6
(a) Find a basis for null A and a basis for im A.
1
0 solvable?
(b) Is the system Ax =
1
[ ]
1
5. The 2 × 2 matrix A has eigenvalue λ1 = 1, corresponding to eigenvector v1 =
, and
0
[ ]
1
eigenvalue λ2 = −1, corresponding to eigenvector v2 =
.
1
(a) Is A diagonalizable?
(b) Find A.
(c) Calculate A2010 .
6. (a) Find symmetric matrices A and B, such that the product AB is not symmetric.
(b) Find eigenvalues and eigenvectors of matrix
2 1 1
1 2 1 .
1 1 2
7. Let M be a Markov matrix, i.e. the sum of the entries of each column is equal to 1. Show
that 1 is an eigenvalue for M .
8. Find an orthonormal basis of the vector space V , generated by vectors
1
1
1
1
1
0
u1 = , u2 = and u3 = .
1
0
1
0
1
1
2
1
0
0
1
0
Which of the vectors a = , b = , c = is an element of V ? Write it as the
1
3
2
3
2
3
linear combination of vectors u1 , u2 and u3 .
9. (a) Prove that matrix A is a positive semidefinite matrix if and only if all of its eigen-
values are nonnegative.
(b) Prove that if A is a positive semidefinite matrix, then there exists positive semidefi-
nite matrix B, such that B 2 = A.
10. Use the least squares method to find the line f (x) = ax + b that fits the best to the points
(−2, 1), (−1, 3), (0, 2), (1, 3) and (2, 1). |
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Časovni pas GMT + 2 uri, srednjeevropski - poletni čas
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Ne, ne moreš dodajati novih tem v tem forumu
Ne, ne moreš odgovarjati na teme v tem forumu
Ne, ne moreš urejati svojih prispevkov v tem forumu
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