Download 3-6 Multiplying Matrices 9-30

Five-Minute Check (over Lesson 3–5)
Then/Now
Example 1: Dimensions of Matrix Products
Key Concept: Multiplying Matrices
Example 2: Multiply Square Matrices
Example 3: Real-World Example: Multiply Matrices
Example 4: Test of the Commutative Property
Example 5: Test of the Distributive Property
Key Concept: Properties of Matrix Multiplication
Over Lesson 3–5
Find D – B.
Find 4B.
Find 2B + 3D.
The table shows weekday ticket
prices for an amusement park.
Ticket prices are doubled on
weekends. Find the weekend
ticket prices and express them as a matrix.
Over Lesson 3–5
Use matrices B and D to find D – B.
A.
C.
B.
D.
Over Lesson 3–5
Use matrices B and D to find 4B.
A.
C.
B.
D.
Over Lesson 3–5
Use matrices B and D to find 2B + 3D.
A.
C.
B.
D.
Over Lesson 3–5
The table shows weekday ticket
prices for an amusement park.
Ticket prices are doubled on
weekends. Find the weekend
ticket prices and express them as a matrix.
A.
B.
C.
D.
You multiplied matrices by a scalar.
• Multiply matrices.
• Use the properties of matrix multiplication.
Dimensions of Matrix Products
A. Determine whether the product of A3×4 and B4×2
is defined. If so, state the dimensions of the
product.
A
3×4
●
B
4×2
=
AB
3×2
Answer: The inner dimensions are equal so the matrix
product is defined. The dimensions of the
product are 3 × 2.
Dimensions of Matrix Products
B. Determine whether the product of A3×2 and B4×3
is defined. If so, state the dimensions of the
product.
A
3×2
●
B
4×3
Answer: The inner dimensions are not equal, so the
matrix product is not defined.
A. Determine whether the matrix product is defined.
If so, what are the dimensions of the product?
A3×2 and B2×3
A. 3 × 3
B. 2 × 2
C. 3 × 2
D. The matrix product is not
defined.
B. Determine whether the matrix product is defined.
If so, what are the dimensions of the product?
A2×3 and B2×3
A. 2 × 3
B. 3 × 2
C. 2 × 2
D. The matrix product is not
defined.
Multiply Square Matrices
Step 1
Multiply the numbers in the first row of R by
the numbers in the first column of S, add the
products, and put the result in the first row,
first column of RS.
Multiply Square Matrices
Step 2
Multiply the numbers in the first row of R by
the numbers in the second column of S, add
the products, and put the result in the first row,
second column of RS.
Multiply Square Matrices
Step 3
Multiply the numbers in the second row of R
by the numbers in the first column of S, add
the products, and put the result in the second
row, first column of RS.
Multiply Square Matrices
Step 4
Multiply the numbers in the second row of R
by the numbers in the second column of S,
add the products, and put the result in the
second row, second column of RS.
A.
B.
C.
D.
Multiply Matrices
CHESS Three teams competed in the final round of
the Chess Club’s championships. For each win, a
team was awarded 3 points and for each draw a
team received 1 point. Which team won the
tournament?
Understand The final scores can be found by
multiplying the wins and draws by the points for each.
Multiply Matrices
CHESS Three teams competed in the final round of
the Chess Club’s championships. For each win, a
team was awarded 3 points and for each draw a
team received 1 point. Which team won the
tournament?
Plan
Write the results from the championship and
the points in matrix form. Set up the matrices
so that the number of rows in the points
matrix equals the number of columns in the
results matrix.
Multiply Matrices
CHESS Three teams competed in the final round of
the Chess Club’s championships. For each win, a
team was awarded 3 points and for each draw a
team received 1 point. Which team won the
tournament?
Results
Points
Multiply Matrices
CHESS Three teams competed in the final round of
the Chess Club’s championships. For each win, a
team was awarded 3 points and for each draw a
team received 1 point. Which team won the
tournament?
Multiply Matrices
CHESS Three teams competed in the final round of
the Chess Club’s championships. For each win, a
team was awarded 3 points and for each draw a
team received 1 point. Which team won the
tournament?
Total Points
Blue
Red
Green
BASKETBALL In Thursday night’s basketball game,
three of the players made the points listed below in
the chart. They scored 1 point for the free-throws,
2 points for the 2-point shots, and 3 points for the
3-points shots. Who scored the most points?
A. Warton
B. Bryant
C. Chris
D. none of the above
Test of the Commutative Property
A. Find KL if K
Answer:
Test of the Commutative Property
B. Find LK if K
So KL ≠ LK. Matrix multiplication is NOT commutative.
A.
B.
C.
D.
A.
B.
C.
D.
Test of the Distributive Property
A.
Answer:
Test of the Distributive Property
Answer:
The Distributive Property works
for matrices.
A.
B.
C.
D.
A.
B.
C.
D.