Translation for "kerroinmatriisin" to english
Translation examples
Tarkastellaan seuraavaksi yhtälöryhmää x + y + 2z = 3 x + y + z = 1 2x + 2y + 2z = 5. Kerroinmatriisiksi saadaan A = , {\displaystyle A={\begin{bmatrix}1&1&2\\1&1&1\\2&2&2\\\end{bmatrix}},} ja täydennetty matriisi on ( A | B ) = . {\displaystyle (A|B)=\left.} Tällä kertaa kerroinmatriisin aste on 2, mutta täydennetyn matriisin 3, joten tällä yhtälöryhmällä ei ole ratkaisuja.
In contrast, consider the system x + y + 2 z = 3 x + y + z = 1 2 x + 2 y + 2 z = 5. {\displaystyle {\begin{aligned}x+y+2z&=3\\x+y+z&=1\\2x+2y+2z&=5.\end{aligned}}} The coefficient matrix is A = , {\displaystyle A={\begin{bmatrix}1&1&2\\1&1&1\\2&2&2\\\end{bmatrix}},} and the augmented matrix is ( A | B ) = . {\displaystyle (A|B)=\left.} In this example the coefficient matrix has rank 2 while the augmented matrix has rank 3; so this system of equations has no solution.
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