Algebra lineare Esempi

$[\begin{array}{c} 0.1 & 0 & 0.1 & 0.1 & 0.2 \\ 0.1 & 0.2 & - 0.1 & 0.1 & - 0.1 \\ 0.1 & - 0.1 & 0.1 & - 0.2 & 0.1 \\ 0.1 & 0.2 & 0.1 & 0.1 & 0.1 \\ 0.1 & 0 & 0 & 0 & 0 \end{array}] \cdot [\begin{array}{c} 0 & 0 & 0 & 0 & 10 \\ 0 & 5 & \frac{10}{3} & \frac{5}{3} & - 10 \\ - 10 & - 15 & - \frac{20}{3} & \frac{35}{3} & 20 \\ 0 & - 5 & - \frac{20}{3} & \frac{5}{3} & 10 \\ 10 & 10 & \frac{20}{3} & \frac{- 20}{3} & - 20 \end{array}]$

Passaggio 1

Sposta il negativo davanti alla frazione.

Passaggio 2

Moltiplica $[\begin{array}{c} 0.1 & 0 & 0.1 & 0.1 & 0.2 \\ 0.1 & 0.2 & - 0.1 & 0.1 & - 0.1 \\ 0.1 & - 0.1 & 0.1 & - 0.2 & 0.1 \\ 0.1 & 0.2 & 0.1 & 0.1 & 0.1 \\ 0.1 & 0 & 0 & 0 & 0 \end{array}] [\begin{array}{c} 0 & 0 & 0 & 0 & 10 \\ 0 & 5 & \frac{10}{3} & \frac{5}{3} & - 10 \\ - 10 & - 15 & - \frac{20}{3} & \frac{35}{3} & 20 \\ 0 & - 5 & - \frac{20}{3} & \frac{5}{3} & 10 \\ 10 & 10 & \frac{20}{3} & - \frac{20}{3} & - 20 \end{array}]$ .

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Passaggio 2.1

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 $5 \times 5$ and the second matrix is $5 \times 5$ .

Passaggio 2.2

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

$[\begin{array}{c} 0.1 \cdot 0 + 0 \cdot 0 + 0.1 \cdot - 10 + 0.1 \cdot 0 + 0.2 \cdot 10 & 0.1 \cdot 0 + 0 \cdot 5 + 0.1 \cdot - 15 + 0.1 \cdot - 5 + 0.2 \cdot 10 & 0.1 \cdot 0 + 0 (\frac{10}{3}) + 0.1 (- \frac{20}{3}) + 0.1 (- \frac{20}{3}) + 0.2 (\frac{20}{3}) & 0.1 \cdot 0 + 0 (\frac{5}{3}) + 0.1 (\frac{35}{3}) + 0.1 (\frac{5}{3}) + 0.2 (- \frac{20}{3}) & 0.1 \cdot 10 + 0 \cdot - 10 + 0.1 \cdot 20 + 0.1 \cdot 10 + 0.2 \cdot - 20 \\ 0.1 \cdot 0 + 0.2 \cdot 0 - 0.1 \cdot - 10 + 0.1 \cdot 0 - 0.1 \cdot 10 & 0.1 \cdot 0 + 0.2 \cdot 5 - 0.1 \cdot - 15 + 0.1 \cdot - 5 - 0.1 \cdot 10 & 0.1 \cdot 0 + 0.2 (\frac{10}{3}) - 0.1 (- \frac{20}{3}) + 0.1 (- \frac{20}{3}) - 0.1 (\frac{20}{3}) & 0.1 \cdot 0 + 0.2 (\frac{5}{3}) - 0.1 (\frac{35}{3}) + 0.1 (\frac{5}{3}) - 0.1 (- \frac{20}{3}) & 0.1 \cdot 10 + 0.2 \cdot - 10 - 0.1 \cdot 20 + 0.1 \cdot 10 - 0.1 \cdot - 20 \\ 0.1 \cdot 0 - 0.1 \cdot 0 + 0.1 \cdot - 10 - 0.2 \cdot 0 + 0.1 \cdot 10 & 0.1 \cdot 0 - 0.1 \cdot 5 + 0.1 \cdot - 15 - 0.2 \cdot - 5 + 0.1 \cdot 10 & 0.1 \cdot 0 - 0.1 (\frac{10}{3}) + 0.1 (- \frac{20}{3}) - 0.2 (- \frac{20}{3}) + 0.1 (\frac{20}{3}) & 0.1 \cdot 0 - 0.1 (\frac{5}{3}) + 0.1 (\frac{35}{3}) - 0.2 (\frac{5}{3}) + 0.1 (- \frac{20}{3}) & 0.1 \cdot 10 - 0.1 \cdot - 10 + 0.1 \cdot 20 - 0.2 \cdot 10 + 0.1 \cdot - 20 \\ 0.1 \cdot 0 + 0.2 \cdot 0 + 0.1 \cdot - 10 + 0.1 \cdot 0 + 0.1 \cdot 10 & 0.1 \cdot 0 + 0.2 \cdot 5 + 0.1 \cdot - 15 + 0.1 \cdot - 5 + 0.1 \cdot 10 & 0.1 \cdot 0 + 0.2 (\frac{10}{3}) + 0.1 (- \frac{20}{3}) + 0.1 (- \frac{20}{3}) + 0.1 (\frac{20}{3}) & 0.1 \cdot 0 + 0.2 (\frac{5}{3}) + 0.1 (\frac{35}{3}) + 0.1 (\frac{5}{3}) + 0.1 (- \frac{20}{3}) & 0.1 \cdot 10 + 0.2 \cdot - 10 + 0.1 \cdot 20 + 0.1 \cdot 10 + 0.1 \cdot - 20 \\ 0.1 \cdot 0 + 0 \cdot 0 + 0 \cdot - 10 + 0 \cdot 0 + 0 \cdot 10 & 0.1 \cdot 0 + 0 \cdot 5 + 0 \cdot - 15 + 0 \cdot - 5 + 0 \cdot 10 & 0.1 \cdot 0 + 0 (\frac{10}{3}) + 0 (- \frac{20}{3}) + 0 (- \frac{20}{3}) + 0 (\frac{20}{3}) & 0.1 \cdot 0 + 0 (\frac{5}{3}) + 0 (\frac{35}{3}) + 0 (\frac{5}{3}) + 0 (- \frac{20}{3}) & 0.1 \cdot 10 + 0 \cdot - 10 + 0 \cdot 20 + 0 \cdot 10 + 0 \cdot - 20 \end{array}]$

Passaggio 2.3

Semplifica ogni elemento della matrice moltiplicando tutte le espressioni.

$[\begin{array}{c} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{array}]$