A good answer might be:

A5×5 B5×3 C3×4 = D5×4.

Distributive Property

The distributive property deals with a matrix expression that contains both matrix multiplication and matrix addition. Go through the following steps to demonstrate the property.

1. Add the right two matrices together, click = to check your result, below.
2. Multiply the first matrix times the result. Click "=" to check your result.

3. Now, work the problem again by forming the product of the left matrix and each of the others.
4. Finally, add up the two products.


Both results are the same, demonstrating that matrix multiplication is distributive over matrix addition:

A(B + C) = AB+AC

It is also true that

(X + Y)Z = XZ+YZ

For more practice, change the elements in the matrices of step 1 (only), and then work the problem again. When you make changes, replace the contents of a cell with an integer (only) and click outside of the cell to make the change.


Calculate the following:

cos w      1 
    0  sin w

x    2 
1    y