More on Matrix Operations

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More on Matrix Operations
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Mastering a Weird Operation
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1) What is the total number of people who vote
for the Democratic party?
(30000)(0.50) (40000)(0.45) (20000)(0.40)
41000
2) What is the total number of people who vote
for the Republican party?
(30000)(0.30) (40000)(0.40) (20000)(0.50)
35000
Observe that multiplying the elements of the row
of B by the elements of the column of A and
adding the results give the number of people who
vote for the Democratic party
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1) We multiply the row of A by the first column
of B and add the results. This is the first
element of AB
2) We multiply the row of A by the second column
of B and add the results. This is the second
element of AB
We repeat this for all the columns of B.
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Example
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1) We multiply the first row of A by each column
of B. This gives the first row of AB.
2) We multiply the second of A by each column of
B. This gives the second row of AB.
We repeat this with all the rows of A.
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Example
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Some Special Matrices
A Zero matrix all its elements are equal to 0.
For instance, here is the 2 x 3 zero matrix
A Square matrix has the same number of rows as
columns.
For instance, here is a 3 x 3 square matrix
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An Identity matrix has 1s on its main diagonal
and 0s everywhere else
For instance, the 2 x 2 identity matrix
For instance, the 3 x 3 identity matrix
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Inverse of a matrix
Example
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So we conclude that B is the inverse of A. We
can write
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Graphing calculators will be used in most cases
to find the inverse of a matrix whenever the
inverse exists.
Example
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A has an inverse but B does not.
Lesson Not every nonzero matrix has an inverse.