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280
T
EACHING
S
UGGESTIONS
Teaching Suggestion M5.1:
Why Discuss Matrices
and Determinants?
These mathematical tools are needed in Markov analysis to com
pute absorbing states. In a more advanced treatment of linear pro
gramming, matrix manipulation skills are also desired.
Teaching Suggestion M5.2:
Matrices Can Be Used to Display
Data in Tabular Form.
As seen in Section M53 in this module, a matrix is also a useful
tool for presenting data.
S
OLUTIONS TO
P
ROBLEMS
M51.
Matrices are used in Markov analysis and game theory.
They may also be used to represent a system of equations in linear
programming.
M52.
One way to calculate the determinant of a matrix is to
draw the primary and secondary diagonals. The numbers in each
diagonal are multiplied. Each of the products found on a pri
mary diagonal are added, and each of the products found on a
secondary diagonal are subtracted. The resulting number is the
determinant.
M53.
Determinants are used in solving a system of equations
and in Fnding the inverse of a matrix.
M54.
A matrix of cofactors is developed as follows:
1.
Select an element in the original matrix.
2.
Draw a line through the row and column of the element
selected. The numbers uncovered represent the cofactor for
that element.
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 Spring '11
 MichaelHanna

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