Transcript Algebra I Remediation

Algebra I Remediation
PRESENTER:
CARLA KIRKLAND
NUMBER SENSE
and
OPERATIONS
Objective 1b
Use matrices to solve mathematical situations
and contextual problems. (DOK 2)
Understand the
Following:
 What is a matrix?
 How to solve word problems
 How to: Add matrices, Subtract
matrices, Perform Scalar
Multiplication
What is a Matrix?
 MATRIX: A
rectangular arrangement
of numbers in rows and
columns.
 The ORDER of a matrix
is the number of the rows
and columns.
 The ENTRIES are the
numbers in the matrix.
 The order of this matrix
is a 2 × 3.
columns
rows
 6 2  1
 2 0 5 


Multiplying a Matrix by a
Scalar

In matrix algebra, a real number is often called a SCALAR. To multiply
a matrix by a scalar, you multiply each entry in the matrix by that
scalar.
 2 0  4(2) 4(0)   8 0 
4





 4  1  4(4) 4(1)  16  4
 1
 2 
 0
 2   4


3   6
 1  4
=  2 
 06

5 


 8 
 2  5 


3  (8) 
 3 3 
=  2

6

5


=  2(3)
  2(6)

 2(3)   6  6


 2(5)  12 10 
3. The matrices below show the different numbers of students
who participated in three of the sports at two high schools.
Which of the following correctly represents the sum of the numbers of
students who participated in the three sports at these two high schools?
MSATP Alg I, Test 1, 1b
Question Number 3
Explanation: Sum of # of students  add matrices
Calculator Key Strokes: Enter North Brook H.S. into matrix A:
x-1
2nd
Pulls up matrix A to edit
ENTER
ENTER
Assigns correct
dimensions to matrix A:
3×2
ENTER
2
8
ENTER
2
3
ENTER
ENTER
2
7
ENTER
1
5
ENTER
3
ENTER
3
1
2
9
2
(Enters in values of North Brook into matrix A)
Enter Memorial H.S. into matrix B:
2nd
3
x-1
ENTER
2
2
ENTER
Pulls up matrix B to edit
Assigns correct
dimensions to matrix B:
3×2
(Enters in values of Memorial H.S. into matrix B)
Answer: C
2nd
MODE
2nd
x-1
Returns to main screen
1
+
2nd
x-1
2
ENTER
2
9
ENTER
2
7
1
ENTER
5
Question Number 3
(Enters in values of North Brook into matrix A)
Alternate Explanation:
Enter Memorial H.S. into matrix B:
Solve by hand:
2nd
x-1
3
ENTER
Memorial
High School
North Brook
High School
2
2
ENTER
Pulls up matrix B to edit
Assigns correct
dimensions to matrix B:
3×2
(Enters in values of Memorial H.S. into matrix B)
+
Answer: C
2nd
=
MODE
2nd
x-1
=
Returns to main screen
1
+
2nd
ENTER
x-1
2
ENTER
15.
Matrix B is the result when matrix A is
multiplied by a scalar.
MSATP Alg I, Test 1, 1b
Question Number 15
Explanation: There is a real number x, that when x is multiplied by A, the result is B,
So, to find y, use proportions:
6
 48  4th entry from A

y  4th entry from B
1st entry from B   4
1st entry from A 
(cross multiply)
6y = -48(-4)
6y 192

6
6
y = 32
Answer: A
×A
MSATP Alg I, Test 1, 1b
Question Number 32
Explanation:
Calculator Key Strokes:
2nd
2
x-1
ENTER
Pulls up matrix A to edit
ENTER
2
ENTER
Assigns 2 × 2 dimensions to A
(Enter values from L into A)
2nd
2
x-1
ENTER
Pulls up matrix B to edit
2
2
ENTER
Assigns 2 × 2 dimensions to B
(Enter values from M into B)
2nd
MODE
2nd
x-1
Answer: D
Returns to main screen
1
–
2nd
x-1
2
ENTER
Computes A-B (or L-M)
2
2
ENTER
ENTER
Assigns 2 × 2 dimensions to A
(Enter values from L into A)
Question Number 32
2nd
x-1
Alternate Explanation:
2
ENTER
Solve by hand:
2
Pulls up matrix B to edit
2
ENTER
Assigns 2 × 2 dimensions to B
(Enter values from M into B)
2nd
2nd
Returns to main screen
MODE
–
x
-1
Answer: D
=
=
1
–
2nd
x
-1
2
ENTER
Computes A-B (or L-M)
43. What values of x, y, z, and w make this matrix
equation true?
MSATP Alg I, Test 1, 1b
Question Number 43
Explanation: The situation is this: A + C = B
Which is the same as: A – B = -C
Let A =
4
3
-2
7
and
B=
5
-2
7
3
Calculator Key Strokes:
2nd
2
x-1
ENTER
2
ENTER
Pulls up matrix A to edit
ENTER
Assigns dimensions to A
2
Pulls up matrix B to edit
ENTER
Assigns dimensions to B
(Enter values for A)
2nd
2
x-1
ENTER
2
(Enter values for B)
2nd
MODE
2nd
x-1
Returns to main screen
1
-1
5
-9
4
-C =
–
2nd
1 -5
C=
9 -4
 x = 1, y = -5, z = 9, w = -4
Answer: B
x-1
2
ENTER
Computes A-B
Question Number 43
Alternate Explanation:
Solve by Hand:
The situation is this: A + C = B
Which is the same as: A – B = -C
Let A =
4
3
-2
7
4
3
-2
7
-C =
=
C=
Answer: B
–
and
5
-2
7
3
B=
=
5
-2
7
3
-C
6. Matrices A and B are shown below.
MSATP, Alg I, Test 2, 1b
Question Number 6
Chooses Matrix A to edit
Explanation:
Calculator Key Strokes:
x-1
2nd
Enters dimensions for Matrix A
3
ENTER
ENTER
3
ENTER
(Enter in values for Matrix A)
x-1
2nd
3
ENTER
Chooses Matrix B to edit
2
3
Enters dimensions for Matrix B
ENTER
(Enter in values for Matrix B)
2nd
2
Answer: H
2nd
MODE
x-1
1
+
2nd
x-1
2
ENTER
Evaluates 2A+B
Question Number 6
Alternate Explanation:
Solve by hand:
+
Question Number 6
Chooses Matrix A to edit
Explanation:
=
Calculator
Key Strokes:
2nd
+
x-1
Enters dimensions for Matrix A
3
ENTER
ENTER
3
ENTER
(Enter in values for Matrix A)
x-1
2nd
=
Chooses Matrix B to edit
2
+
3
ENTER
3
Enters dimensions for Matrix B
ENTER
(Enter in values for Matrix B)
=
2nd
2
Answer: H
2nd
MODE
x-1
1
+
2nd
x-1
2
ENTER
Evaluates 2A+B
36.
Andrew plans to buy 3 T-shirts and 3 sweaters. The price in dollars,
including tax, of each T-shirt and sweater is shown in matrix C. The store
is offering a 15% discount on all the items.
Andrew determined the sale price of each item as shown in the matrix
below.
Which operation justifies the sale price of each item he plans to buy?
MSATP, Alg I, Test 2,1b
Question Number 36
Explanation:
Notice there is no need to enter in matrix values, etc., because this is simply a matter of
understanding “% discount”
Cost is given (c)
“15% discount” means: find 15% of cost
0.15C
Subtract (15% of cost) from the cost (c)
C – 0.15c
Answer: H
24 Matrix R is shown below.
Which matrix represents -6R?
MSATP Alg I, Test 3, 1B
Question Number 24
Explanation: Multiply each element in Matrix R by -6.
Answer: G
Alternate Explanation:
Solve by hand:
=
=Question Number 24
Explanation: Multiply each element in Matrix R by -6.
Answer: G