PRESENTER:CARLA KIRKLAND

Algebra I Remediation

NUMBER SENSE and

OPERATIONS

Objective 1b

Use matrices to solve mathematical situations and contextual problems. (DOK 2)

What is a matrix?

How to solve word problems

How to: Add matrices, Subtract matrices, Perform Scalar Multiplication

Understand the Following:

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.

502

126rows

columns

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.

416

08

)1(4)4(4

)0(4)2(4

14

024

86

54

30

212

=

)8(360

52412

=

=

56

332

1012

66

)5(2)6(2

)3(2)3(2

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:

Answer: C

2nd x-1 ENTER Pulls up matrix A to edit

3 ENTER 2 ENTER Assigns correct dimensions to matrix A: 3 × 2

2 2 ENTER 3 ENTER 1 ENTER 8 3

(Enters in values of North Brook into matrix A)

Enter Memorial H.S. into matrix B:

2nd x-1 2 Pulls up matrix B to edit

3 ENTER 2 ENTER Assigns correct dimensions to matrix B: 3 × 2

(Enters in values of Memorial H.S. into matrix B)

2nd MODE Returns to main screen

2nd x-1 1 + 2nd x-1 2 ENTER

2 2 7 ENTER 9 1 ENTER 5 ENTER

Question Number 3 Alternate Explanation: Solve by hand:

North Brook High School

Memorial High School

+ = =

Question Number 3

Explanation: Sum of # of students add matrices

Calculator Key Strokes: Enter North Brook H.S. into matrix A:

Answer: C

2nd x-1 ENTER Pulls up matrix A to edit

3 ENTER 2 ENTER Assigns correct dimensions to matrix A: 3 × 2

2 2 ENTER 3 ENTER 1 ENTER 8 3

(Enters in values of North Brook into matrix A)

Enter Memorial H.S. into matrix B:

2nd x-1 2 Pulls up matrix B to edit

3 ENTER 2 ENTER Assigns correct dimensions to matrix B: 3 × 2

(Enters in values of Memorial H.S. into matrix B)

2nd MODE Returns to main screen

2nd x-1 1 + 2nd x-1 2 ENTER

2 2 7 ENTER 9 1 ENTER 5 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:

y

48

4

6

(cross multiply)

6y = -48(-4)

6

192

6

6y

y = 32

Answer: A

× A

1st entry from A

1st entry from B

4th entry from A

4th entry from B

MSATP Alg I, Test 1, 1b

Question Number 32

Explanation:

Calculator Key Strokes:

Answer: D

2nd x-1 ENTER

2

ENTER 2 ENTER

ENTER 2 2 ENTER

2nd x-1 2

MODE 2nd

2nd x-1 1 – 2nd x-1 2 ENTER

(Enter values from L into A)

(Enter values from M into B)

Pulls up matrix A to edit

Assigns 2 × 2 dimensions to A

Pulls up matrix B to edit

Assigns 2 × 2 dimensions to B

Returns to main screen

Computes A-B (or L-M)

Question Number 32 Alternate Explanation: Solve by hand:

– = =

Question Number 32

Explanation:

Calculator Key Strokes:

Answer: D

2nd x-1 ENTER

2

ENTER 2 ENTER

ENTER 2 2 ENTER

2nd x-1 2

MODE 2nd

2nd x-1 1 – 2nd x-1 2 ENTER

(Enter values from L into A)

(Enter values from M into B)

Pulls up matrix A to edit

Assigns 2 × 2 dimensions to A

Pulls up matrix B to edit

Assigns 2 × 2 dimensions to B

Returns to main screen

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 = and B =

Calculator Key Strokes:

Answer: B

4 3

-2 7

5 -2

7 3

-C =

2nd x-1 ENTER

2

ENTER 2 ENTER

ENTER 2 2 ENTER

2nd x-1 2

MODE 2nd

2nd x-1 1 – 2nd x-1 2 ENTER

(Enter values for A)

(Enter values for B)

Pulls up matrix A to edit

Assigns dimensions to A

Pulls up matrix B to edit

Assigns dimensions to B

Returns to main screen

Computes A-B

-1 5

- 9 4

1 -5

9 -4 C =

x = 1, y = -5, z = 9, w = -4

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 = and B =

Answer: B

4 3

-2 7

5 -2

7 3

4 3

-2 7 –

5 -2

7 3 = -C

-C =

=

C =

MSATP, Alg I, Test 2, 1b

6. Matrices A and B are shown below.

Question Number 6

Explanation:

Calculator Key Strokes:

(Enter in values for Matrix A)

(Enter in values for Matrix B)

2nd x-1 ENTER 3 ENTER 3 ENTER

Chooses Matrix A to edit Enters dimensions for Matrix A

3 ENTER 3 ENTER Enters dimensions for Matrix B

Chooses Matrix B to edit

2nd x-1 2nd ENTER 2 + x-1 2 Evaluates 2A+B

Answer: H

2nd x-1 2

2nd MODE

1

Question Number 6 Alternate Explanation: Solve by hand:

Question Number 6

Explanation:

Calculator Key Strokes:

(Enter in values for Matrix A)

(Enter in values for Matrix B)

2nd x-1 ENTER 3 ENTER 3 ENTER

Chooses Matrix A to edit Enters dimensions for Matrix A

3 ENTER 3 ENTER Enters dimensions for Matrix B

Chooses Matrix B to edit

2nd x-1 2nd ENTER 2 + x-1 2 Evaluates 2A+B

Answer: H

2nd x-1 2

2nd MODE

1

+

= +

= +

=

MSATP, Alg I, Test 2,1b

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?

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