UPSKILL MATH PLUS

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Theory:

Distributive property:
1. Distributive property of scalar and two matrices - \(p(A+B) = pA+ pB\)
 
Let \(A\), and \(B\) be \(m×n\) matrices and \(p\) and \(q\) be two non-zero scalars (numbers).
Example:
Consider the matrices \( A = \begin{bmatrix}
1 & 2 \\ 
3 & 4
\end{bmatrix}, B = \begin{bmatrix}
5 & 6\\
7 & 8
\end{bmatrix}\) and \(p = 2\) then verify \(p(A+B) = pA+ pB\).
 
Solution:
 
distributive_property_of_scalar_and_two_matrices.png
 
2. Distributive property of two scalars with a matrix - \((p +q)A = pA +qA\)
Example:
Let's take the same matrices to prove \(A = \begin{bmatrix}
1 & 2 \\ 
3 & 4
\end{bmatrix}\) to prove \((p +q)A = pA +qA\). Where \( p = 2\) , and \( q = 4\).
 
Solution:
 
distributive_property_of_two_scalars_with_the_matrix.png