UPSKILL MATH PLUS

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Learn more### 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 \(p(A+B) = pA+ pB\).

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**:

**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 \( q = 4\).

1 & 2 \\

3 & 4

\end{bmatrix}\) to prove \((p +q)A = pA +qA\). Where \( p = 2\) , and \( q = 4\).

**Solution**: