... Se numeste matrice cu m linii si n coloane sau de tip EMBED Equation.3 un tablou cu m linii si n coloane EMBED Equation.3 ale carui elemente EMBED Equation.3 sunt numere complexe.Uneori aceasta matrice se noteaza si EMBED Equation.3 unde EMBED Equation.3 si EMBED Equation.3 . Pentru elementul EMBED Equation.3 , indicele i arata linia pe care se afla elementul, iar al doilea indice j indica pe ce coloana este situat.Multimea matricilor de tip EMBED Equation.3 cu elemente numere reale se noteaza prin EMBED Equation.3 . Aceleasi semnificatii au si multimile EMBED Equation.3 , EMBED Equation.3 , EMBED Equation.3 .Cazuri particulare1 O matrice de tipul EMBED Equation.3 deci cu o linie si n coloane se numeste matrice linie si are forma EMBED Equation.3 .2 O matrice de tipul EMBED Equation.3 cu m linii si o coloana se numeste matrice coloana si are forma EMBED Equation.3 .3 O matrice de tip EMBED Equation.3 se numeste nula zero daca toate elementele ei sunt zero. Se noteaza cu O EMBED Equation.3 .4 Daca numarul de linii este egal cu numarul de coloane, atunci matricea se numeste patratica. EMBED Equation.3 .Sistemul de elemente EMBED Equation.3 reprezinta diagonala principala a matricii A, iar suma acestor elemente EMBED Equation.3 se numeste urma matricii A notata TrA EMBED Equation.3 . Sistemul de elemente EMBED Equation.3 reprezinta diagonala secundara a matricii A.Multimea acestor matrici se noteaza EMBED Equation.3 . Printre aceste matrici una este foarte importanta aceasta fiind EMBED Equation.3 si se numeste matricea unitate pe diagonala principala are toate elementele egale cu 1, iar in rest sunt egale cu 0.1.2. Operatii cu matrici1.2.1. Egalitatea a doua matriciDefinitie. Fie EMBED Equation.3 , EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 . Spunem ca matricile A, B sunt egale si scriem A B daca EMBED Equation.3 EMBED Equation.3 , EMBED Equation.3 EMBED Equation.3 , EMBED Equation.3 EMBED Equation.3 .Exemplu Sa se determine numerele reale x, y astfel incat sa avem egalitatea de matrici EMBED Equation.3 .R. Matricile sunt egale daca elementele corespunzatoare sunt egale, adica EMBED Equation.3 Rezolvand acest sistem gasim solutia x 1, y -3.1.2.2. Adunarea matricilorDefinitie. Fie EMBED Equation.3 , EMBED Equation.3 , EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 . Matricea C se numeste suma matricilor A, B daca EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 , EMBED Equation.3 EMBED Equation.3 , EMBED Equation.3 EMBED Equation.3 .Observatii1 Doua matrici se pot aduna daca sunt de acelasi tip, adica daca au acelasi numar de linii si acelasi numar de coloane, deci A, B EMBED Equation.3 EMBED Equation.3 .2 Explicit adunarea matricilor A, B inseamna EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 .Exemplu Sa se calculeze A B pentru1. EMBED Equation.3 2. EMBED Equation.3 R. 1. Avem EMBED Equation.3 2. Avem EMBED Equation.3 .Proprietati ale adunarii matricilor EMBED Equation.3 Asociativitatea adunarii. Adunarea matricilor este asociativa, adica EMBED Equation.3 , EMBED Equation.3 A, B, C EMBED Equation.3 EMBED Equation.3 . EMBED Equation.3 Comutativitatea adunarii. Adunarea matricilor este comutativa, adica EMBED Equation.3 , EMBED Equation.3 A, B EMBED Equation.3 EMBED Equation.3 . EMBED Equation.3 Element neutru. Adunarea matricilor admite matricea nula ca element neutru, adica EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Eq...
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