Verify the distributive property — task. Mathematics State Board, Class 10.

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Answer variants:

[\begin{array}{l} 6 & 6 & 0 \\ 6 & -10 & -8 \\ 4 & -10 & -22 \end{array}]

[\begin{array}{l} 14 & 20 & 22 \\ 20 & 0 & -20 \\ -4 & -20 & 0 \end{array}]

[\begin{array}{l} 14 & 20 & 22 \\ 18 & 10 & -20 \\ -4 & 0 & -28 \end{array}]

[\begin{array}{l} 7 & 10 & 11 \\ 9 & 5 & -10 \\ -2 & 0 & -14 \end{array}]

[\begin{array}{l} 8 & 14 & 22 \\ 12 & 20 & -12 \\ -8 & 10 & -6 \end{array}]

Check the distributive property \(p(A+B) = pA+ pB\) of the given matrices, where \( p = 2\).

If \(A =\begin{bmatrix}
4 & 7 & 11\\
6 & 10 & -6\\
-4 & 5 & -3
\end{bmatrix}, B = \begin{bmatrix}
3 & 3 & 0\\
3 & -5 & -4\\
2 & -5 & -11
\end{bmatrix}\)

\(A + B\) matrix is

\(p(A + B)\) matrix is

\(pA\) matrix is

\(pB\) matrix is

\(pA+ pB\) matrix is

The distributive property of the matrix \(p(A+B)\) \(pA+ pB\)

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14. Verify the distributive property

Exercise condition: