Download 4-2

4-2
4-2 Multiplying
MultiplyingMatrices
Matrices
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
22
4-2 Multiplying Matrices
Warm Up
1. What are the dimensions of A? 3  2
2. What is entry D12? –2
Evaluate if possible.
3. 2A — C
4. C + 2D
Not possible
Holt Algebra 2
5. 10(2B + D)
4-2 Multiplying Matrices
Objectives
Understand the properties of matrices
with respect to multiplication.
Multiply two matrices.
Holt Algebra 2
4-2 Multiplying Matrices
Vocabulary
matrix product
square matrix
main diagonal
multiplicative identity matrix
Holt Algebra 2
4-2 Multiplying Matrices
An m  n matrix A can be identified by using the
notation Am  n.
Holt Algebra 2
4-2 Multiplying Matrices
Example 1A: Identifying Matrix Products
Tell whether the product is defined. If so, give
its dimensions.
A3  4 and B4  2; AB
A
34
B
42=
AB
3  2 matrix
The inner dimensions are equal (4 = 4), so the matrix
product is defined. The dimensions of the product are
the outer numbers, 3  2.
Holt Algebra 2
4-2 Multiplying Matrices
Example 1B: Identifying Matrix Products
Tell whether the product is defined. If so, give
its dimensions.
C1  4 and D3  4; CD
C
D
14
34
The inner dimensions are not equal (4 ≠ 3), so the
matrix product is not defined.
Holt Algebra 2
4-2 Multiplying Matrices
Check It Out! Example 1c
Tell whether the product is defined. If so, give
its dimensions.
P2  5
Q5  3
R4  3
S4  5
SQ
S
45
Q
53
The inner dimensions are equal (5 = 5), so the matrix
product is defined. The dimensions of the product are
the outer numbers, 4  3.
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A: Finding the Matrix Product
Find the product, if possible.
WX
Check the dimensions. W is 3  2 , X is 2  3 .
WX is defined and is 3  3.
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 1 of W and column 1 of X as shown.
Place the result in wx11.
3(4) + –2(5)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 1 of W and column 2 of X as shown.
Place the result in wx12.
3(7) + –2(1)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 1 of W and column 3 of X as shown.
Place the result in wx13.
3(–2) + –2(–1)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 2 of W and column 1 of X as shown.
Place the result in wx21.
1(4) + 0(5)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 2 of W and column 2 of X as shown.
Place the result in wx22.
1(7) + 0(1)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 2 of W and column 3 of X as shown.
Place the result in wx23.
1(–2) + 0(–1)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 3 of W and column 1 of X as shown.
Place the result in wx31.
2(4) + –1(5)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 3 of W and column 2 of X as shown.
Place the result in wx32.
2(7) + –1(1)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2A Continued
Multiply row 3 of W and column 3 of X as shown.
Place the result in wx33.
2(–2) + –1(–1)
Holt Algebra 2
4-2 Multiplying Matrices
Example 2B: Finding the Matrix Product
Find each product, if possible.
XW
Check the dimensions. X is 2  3, and W is 3  2 so
the product is defined and is 2  2.
Holt Algebra 2
4-2 Multiplying Matrices
Check It Out! Example 2a
Find the product, if possible.
BC
Check the dimensions. B is 3  2, and C is 2  2 so
the product is defined and is 3  2.
Holt Algebra 2
4-2 Multiplying Matrices
Lesson Quiz
Evaluate if possible.
1. AB
2. BA
3. A2
4. BD
5. C3
Holt Algebra 2
4-2 Multiplying Matrices
Lesson Quiz
Evaluate if possible.
1. AB
2. BA
3. A2
not possible
4. BD
not possible
5. C3
Holt Algebra 2