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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. Perform the matrix addition. Click = to check your result under step 2, below.


2. Multiply the two matrices. Click "=" to see the final result.

3. Now, work the problem again in a different order. First form the product of the left matrix with each of the other two.


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 and click outside of the cell to make the change.


Calculate the following:

cos w      1 
    0  sin w

x    2 
1    y