MATEMATICA 2 – TEMA 1˘ · PDF fileMATEMATICA 2 – TEMA 1˘ Problema 1....
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Transcript of MATEMATICA 2 – TEMA 1˘ · PDF fileMATEMATICA 2 – TEMA 1˘ Problema 1....
MATEMATICA 2 – TEMA 1
Problema 1. Reduceti urmatoarele matrice la formele esalon corespunzatoare,apoi identificati pivotii si precizati rangul fiecarei matrice:
a)
0 −3 −6 4 9−1 −2 −1 3 1−2 −3 0 3 −11 4 5 −9 −7
; b)
0 3 −6 6 4 −53 −7 8 −5 8 93 −9 12 −9 6 15
.
Problema 2. Folosind metoda lui Gauss, rezolvati sistemele:
a)
5x1 − x2 + 2x3 = 7
−2x1 + 6x2 + 9x3 = 0
−7x1 + 5x2 − 3x3 = 5
; b)
x1 − 2x2 − 6x3 = 12
2x1 + 4x2 + 12x3 = −17
x1 − 4x2 − 12x3 = 22
;
c)
x1 + x2 + 2x3 − 5x4 = 3
2x1 + 5x2 − x3 − 9x4 = −3
2x1 + x2 − x3 + 3x4 = −11
x1 − 3x2 + 2x3 + 7x4 = −5
;
d)
x1 + 2x2 + x3 + 2x4 + x5 = 1
2x1 + 4x2 + 4x3 + 6x4 + x5 = 2
3x1 + 6x2 + x3 + 4x4 + 5x5 = 4
x1 + 2x2 + 3x3 + 5x4 + x5 = 4
.
Problema 3. Folosind descompunerea LU , rezolvati sistemele:
a)
3x− 2y + 2z = 9
x− 2y + z = 5
2x− y − 2z = −1
; b)
x− 3y + z = 4
2x− 8y + 8z = −2
6x− 3y + 15z = −9
.
Problema 4. Folosind metoda Gauss-Jordan, aflati inversele matricelor:
a) A =
2 −1 0−1 2 −10 −1 2
; b) B =
3 2 −11 −1 22 3 −1
;
c) C =
4 8 −7 142 5 −4 60 2 1 −73 6 −5 10
.