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## Multiplying Matrices

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### Multiplying Matrices Algebra 2 Section 3.6 Recall: Scalar Multiplication - each element in a matrix is multiplied by a constant. Multiplying one matrix by another ... – PowerPoint PPT presentation

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Title: Multiplying Matrices

1
Multiplying Matrices
Algebra 2Section 3.6
2
Recall Scalar Multiplication - each element in
a matrix is multiplied by a constant.
Multiplying one matrix by another has a few more
rules to follow
3
The product of two matrices is defined if the
number of columns in the 1st matrix is equal to
the number of rows in the 2nd matrix.
These must match.
4
Multiply.
Can these be multiplied? Check the order of each!
Dimensions (order) 2 x 3 2 x 2
They dont match so these cannot be multiplied
together.
5
Examples
Can these be multiplied? Check the order of each!
Yes, they can!!
Now multiply each row of the 1st matrix by each
column of the 2nd matrix
2(3) -1(5)
2(-9) -1(7)
2(2) -1(-6)
3(-9) 4(7)
3(2) 4(-6)
3(3) 4(5)
6
Multiply.
Answer should be a 2 x 2
0(4) (-1)(-2)
0(-3) (-1)(5)
1(4) 0(-2)
1(-3) 0(5)
7
Multiply.
8
On a side note
We can use matrices to write a system of
equations.
This is useful when solving augmented matrices.
9
Multiplying Matrices Song
• (to the tune of Oh my Darling, Clementine)
• Row by column, row by column
• Multiply them line by line
• Add the products for an entry
• Now youre doing it just fine

10
Homework
• p. 199-200
• 6-15 multiples of 3,
• 20, 22, 30