Matemática discreta Exemplos

${[\begin{array}{c} a b & b^{2} \\ - a^{2} & a b \end{array}]}^{2}$

Etapa 1

To evaluate a square matrix to a positive integer power $n$ , multiply $n$ copies of the matrix.

$[\begin{array}{c} a b & b^{2} \\ - a^{2} & a b \end{array}] \cdot [\begin{array}{c} a b & b^{2} \\ - a^{2} & a b \end{array}]$

Etapa 2

Multiplique $[\begin{array}{c} a b & b^{2} \\ - a^{2} & a b \end{array}] [\begin{array}{c} a b & b^{2} \\ - a^{2} & a b \end{array}]$ .

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Etapa 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 $2 \times 2$ and the second matrix is $2 \times 2$ .

Etapa 2.2

Multiplique cada linha na primeira matriz por cada coluna na segunda matriz.

$[\begin{array}{c} a b (a b) + b^{2} (- a^{2}) & a b \cdot b^{2} + b^{2} (a b) \\ - a^{2} (a b) + a b (- a^{2}) & - a^{2} b^{2} + a b (a b) \end{array}]$

Etapa 2.3

Simplifique cada elemento da matriz multiplicando todas as expressões.

$[\begin{array}{c} 0 & 2 a b^{3} \\ - 2 a^{3} b & 0 \end{array}]$