Matematika Berhingga Contoh

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 3 & - 4 \\ - 5 & 7 \end{array}] [\begin{array}{c} m \\ n \end{array}]$

Langkah 1

Kalikan $[\begin{array}{c} 3 & - 4 \\ - 5 & 7 \end{array}] [\begin{array}{c} m \\ n \end{array}]$ .

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Langkah 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 $2 \times 1$ .

Langkah 1.2

Kalikan setiap baris pada matriks pertama dengan setiap kolom pada matriks kedua.

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 3 m - 4 n \\ - 5 m + 7 n \end{array}]$

Langkah 2

Write as a linear system of equations.

$x = 3 m - 4 n$

$y = - 5 m + 7 n$

Langkah 3

Kurangi sistem.

$x = 3 m - 4 n, y = - 5 m + 7 n$