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A trucking company uses matrix A , shown below, to represent the driving time in hours for 6 trucking routes. A = [ 4 6 8 ]
[6 8 10 ]
The driving time matrix is based on an average speed of 60 miles per hour. This means that the matrix 60 A represents the driving distances in miles for these 6 trucking routes. Which of these is the matrix 60 A ?

Answer :

Each element of the matrix are multiplied by the scalar to form a matrix of

same size as the original matrix in matrix scalar multiplication.

  • [tex]60 \cdot A = \left[\begin{array}{ccc}240\4&360&480\\360&480&600\end{array}\right][/tex]

Reasons:

The matrix A is presented as follows;

[tex]A = {\left[\begin{array}{ccc}4&6&8\\6&8&10\end{array}\right]}[/tex]

Using the multiplication of a matrix and a scalar, we have;

[tex]60 \cdot A = 60 \cdot \left[\begin{array}{ccc}4&6&8\\6&8&10\end{array}\right] = \left[\begin{array}{ccc}60 \times 4&60 \times 6&60 \times 8\\60 \times 6&60 \times 8&60 \times 10\end{array}\right] = \left[\begin{array}{ccc}\mathbf{240}&\mathbf{360}&\mathbf{480}\\\mathbf{360}&\mathbf{480}&\mathbf{600}\end{array}\right][/tex]

Therefore;

[tex]60 \cdot A = \left[\begin{array}{ccc}240\4&360&480\\360&480&600\end{array}\right][/tex]

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