CK12 - Geometry

Notethat in scalarmultiplication:

• any matrixcan be multipliedby any real number


• the productis a matrix


• the producthas the samedimensionsas the originalmatrix

Example 1

Let ,and

Whatis the scalarproduct?

Let’s continuean examplefrom an earlierlesson.

Example 2

A companyhas two warehousesin their easternregion,wherethey storethreemodelsof their product.A

matrixcan representthe numbersof eachmodelavailablein eachwarehouse.

EasternRegion

Model

Warehouse

Herethe row numberof an elementrepresentsthewarehousenumber, and thecolumnnumberrepresents
themodelnumber.

Supposethat managersdecideto increasethe numberof eachmodelin eachwarehouseby. After
the increasetherewill be threetimesas manyof eachmodelin eachwarehouse.

A scalarproductcan representthis situationvery precisely. Let be the matrixthat representsthe distri-
butionof itemsby modeland warehouseafterthe increase.

For instance,after the increasetherewill be Model itemsin Warehouse.

ScalarProductsfor Dilations

Recallfrom the DilationRefresherabove: