Matematica discreta Esempi

$[\begin{array}{c} - 6 & 3 \\ 3 & 5 \end{array}] [\begin{array}{c} x & - 2 \\ y & - 6 \end{array}] = [\begin{array}{c} 27 & - 6 \\ - 7 & - 36 \end{array}]$

Passaggio 1

Moltiplica $[\begin{array}{c} - 6 & 3 \\ 3 & 5 \end{array}] [\begin{array}{c} x & - 2 \\ y & - 6 \end{array}]$ .

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Passaggio 1.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is $2 \times 2$ and the second matrix is $2 \times 2$ .

Passaggio 1.2

Moltiplica ogni riga nella prima matrice per ogni colonna nella seconda matrice.

$[\begin{array}{c} - 6 x + 3 y & - 6 \cdot - 2 + 3 \cdot - 6 \\ 3 x + 5 y & 3 \cdot - 2 + 5 \cdot - 6 \end{array}] = [\begin{array}{c} 27 & - 6 \\ - 7 & - 36 \end{array}]$

Passaggio 1.3

Semplifica ogni elemento della matrice moltiplicando tutte le espressioni.

$[\begin{array}{c} - 6 x + 3 y & - 6 \\ 3 x + 5 y & - 36 \end{array}] = [\begin{array}{c} 27 & - 6 \\ - 7 & - 36 \end{array}]$

Passaggio 2

Write as a linear system of equations.

$- 6 x + 3 y = 27$

$- 6 = - 6$

$3 x + 5 y = - 7$

$- 36 = - 36$

Passaggio 3

Since $- 36 = - 36$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.