Determinanţi
2
Determinanti 1. | x 1 0 2 −1 3 1 0 −1 | =2 | x 1 x 2 −1 5 −1 0 0 | =2 | 1 x −1 5 | =2= ¿ 5 +x=2=¿ x=−3 2. d= | x 1 x 2 x 3 x 2 x 3 x 1 x 3 x 1 x 2 | ;x 1 ,x 2 ,x 3 rădăcinialeecuaţiei : x 3 −3 x 2 ++3 x + 5=0 x 1 + x 2 +x 3 =3 x 1 x 2 + x 1 x 3 +x 2 x 3 =3 x 1 x 2 x 3 =−5 d= | x 1 + x 2 +x 3 x 2 x 3 x 1 + x 2 +x 3 x 3 x 1 x 1 + x 2 +x 3 x 1 x 2 | =3 | 1 x 2 x 3 1 x 3 x 1 1 x 1 x 2 | =3 | 1 x 2 x 3 0 x 3 −x 2 x 1 −x 3 0 x 1 −x 2 x 2 −x 3 | 3 | x 3 −x 2 x 1 −x 3 x 1 −x 2 x 2 −x 3 | =3 ( x 3 x 2 −x 3 2 −x 2 2 +x 2 x 3 −x 1 2 +x 1 x 3 +x 1 x 2 −x 2 x 3 ) =¿ ¿ 3 ( 3−x 1 2 −x 2 2 −x 3 2 ) =3 ( 3−3) =0 x 1 2 + x 2 2 +x 3 2 = ( x 1 +x 2 +x 3 ) 2 −2 ( x 1 x 2 +x 1 x 3 + x 2 x 3 ) 3. Folosind proprietătile determinantilor să se demonstreze următoarea inegalitate: d= | 1−a−b c c a 1−b−c a b b 1−c−a | ≥ 0 d= | 1 1 1 a 1−b−c a b b 1−c−a | = | 1 0 0 a 1−a−b−c 0 b 0 1−a−b− c | =( 1−a−b−c) 2 ≥ 0
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Transcript of Determinanţi
Determinanti
1. 2.
3. Folosind propriettile determinantilor s se demonstreze urmtoarea inegalitate:
4. Folosind propriettile deteminantilor, s se verifice urmtoarea egalitate:
