determinant

# determinant - Determinandid: omadused, arvutamine....

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Unformatted text preview: Determinandid: omadused, arvutamine. Pöördmaatriks: olemasolu, leidmine. K˜orgema matemaatika p˜ohikursus. TE. 0589 Determinandid: omadused, arvutamine. P ¨o ¨ordmaatriks: olemasolu, leidmine. – p. 1/ 9 Determinandi mõiste Esimest järku determinant Arvu a determinandi | a | ehk esimest järku determinandi defineeritakse valemiga | a | = det a = a. Determinandid: omadused, arvutamine. P ¨o ¨ordmaatriks: olemasolu, leidmine. – p. 2/ 9 Determinandi mõiste Esimest järku determinant Arvu a determinandi | a | ehk esimest järku determinandi defineeritakse valemiga | a | = det a = a. Teist järku determinant Teist järku ruutmaatriksi A =   a 11 a 12 a 21 a 22   determinant on defineeritud arendusvalemiga | A | = det A = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle a 11 a 12 a 21 a 22 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = a 11 a 22 − a 12 a 21 . Determinandid: omadused, arvutamine. P ¨o ¨ordmaatriks: olemasolu, leidmine. – p. 2/ 9 Kolmandat järku determinant Kolmandat järku ruutmaatriksi A =     a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33     determinandiks on | A | = det A = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = a 11 a 22 a 33 + a 12 a 23 a 31 + a 21 a 32 a 13 − a 31 a 22 a 13 − a 12 a 21 a 33 − a 11 a 23 a 32 . Determinandid: omadused, arvutamine. P ¨o ¨ordmaatriks: olemasolu, leidmine. – p. 3/ 9 Miinor ja algebraline täiend Olgu A n-järku ruutmaatriks A =         a 11 a 12 ... a 1 n a 21 a 22 ... a 2 n . . . . . . . . . a n 1 a n 2 ... a nn         . Determinandid: omadused, arvutamine. P ¨o ¨ordmaatriks: olemasolu, leidmine. – p. 4/ 9 Miinor ja algebraline täiend Olgu A n-järku ruutmaatriks A =         a 11 a 12 ... a 1 n a 21 a 22 ... a 2 n . . . . . . . . . a n 1 a n 2 ... a nn         ....
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