Calculating the Determinant of a 3 by 3 Matrix

Calculating the Determinant of a3 by 3 Matrix

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This Concept tutor is a supplement to help you understand the process of calculating a determinant of a matrix. You will use a four step process.

Applications of Matrices in Real-Life

Used in real life applications (finance, science, manufacturing, optimizing, etc) to solve linear systems of equations.

Delta Air Lines uses linear programming (based on matrix computations) to solve its flight scheduling problem. The problem is to match aircraft to flight legs and fill seats with paying passengers, there by reducing the operating cost.

Applications of Matrices in Real-Life

Matrices are used with encryption in wi-fi communication . When you connect to a wi-fi hub in a restaurant , matrices and their inverses are used to encrypt your message.

Click here to watch the Introduction

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Video on Introduction to a 3 x 3 matrix

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638

23815645

311

A =

(1) What is a32 in the Matrix A?

3 3238

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A) B) C)Select one of the following three options:

Now it's your turn

If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

531

652

321

B =

(2) What is b21 in the Matrix B?

2 12

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A) B) C)Select one of the following three options:

If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

Now it's your turn

625

351

321

C =

(3) What is c23 in the Matrix C?

3 23

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A) B) C)Select one of the following three options:

Now it's your turn

Click here for the Definition video Part 1

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Step 1: Definition of determinant and minor

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333231

232221

131211

www

www

www

W =

(4) What is the M12 (minor row 1, column 2 ) ?

3332

2322

ww

ww

3331

2321

ww

ww

3231

2221

ww

ww

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A) B) C)

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Now it's your turn

Select one of the following three options:

Click here for the Definition video Part 2

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Step 2: Applying Definition to a Matrix

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(-1)1+3 *w13*3331

2321

ww

ww

333231

232221

131211

www

www

www

|W|=

(5) What is the 3rd term in computing the Determinant W as shown below?

(-1)1+3 *w13*3231

2221

ww

ww

=(-1)1+1 *w11*3332

2322

ww

ww+ (-1)1+2 *w12*

3331

2321

ww

ww

(-1)2+3 *w13*3231

2221

ww

ww

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+ ??

A) B)

C)NEXT

Select one of the following three options:

Now it's your turn

Click here for the Definition video Part 3

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Step 3: Solving the Minor of a Matrix

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d11 d12

|D| = d21 d22

|D|= (-1)1+3 d11 d22 + (-1) 1+3 d12 d21

|D|= (-1)1+2 d11 d21 + (-1) 1+1 d12 d22

|D|= (-1)1+1 d11 d22 + (-1) 1+2 d12 d21

(6)What is the determinant of the 2 by 2 matrix D?

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A)

B)

C)

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Now it's your turn

Select one of the following three options:

If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

-1 2G = -2 1

(7) What is the determinant of a 2 by 2 matrix?

35

-5

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A)

B)

C)

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Select one of the following three options:

Now it's your turn

Click here for the Definition video Part 4

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Step 4: Final Step in Computing Determinant of a Matrix

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Click here for the Example video Part 1

Applying the Concept to Solving a Numerical Problem

Step 1: First term of summation and Identifying the Minor

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638

23815645

311

A =

(8) What is M32 (minor 3, 2 ) in the Matrix A?

15645

11 38

11

23845

31 A) B) C)

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Select one of the following three options:

Now it's your turn

If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

531

652

321

B =

(9) What is M21 (minor row 2, column 1 ) in the Matrix B?

53

32

53

65

31

21

A) B) C)

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Now it's your turn

Select one of the following three options:

If you get the answer correct, you will go to master the next step. If you make a mistake, the system will take you to solve another problem.

625

351

321

C =

(10) What is M23 (minor row 2, column 3 ) in the Matrix C?

51

21

62

21

25

21

A) B) C)

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Now it's your turn

Select one of the following three options:

Applying the Concept to Solving a Numerical Problem

Step 2: Writing the Summation Equation

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Click here for the Example video Part 2

(-1)1+3 *(1)*11-

14

(11) What is the 3rd term of summation of the determinant of W?

(-1)1+3 *(1)*1-6

42

(-1)2+3 *(1)*1-6

42

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+ ?

A) B)

C)

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116

142

142

= (-1)1+1*(2)* + (-1)1+2*(-4)*

11

14

16

12IWI =

Now it's your turn

Select one of the following three options:

Applying the Concept to Solving a Numerical Problem

Step 3: Final solution

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Click here for the Example video Part 3

328

526

311

z =

(12) Compute the determinant of the Matrix Z?

A) B) C)

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Now it’s your turn

Select one of the following three options:

-70 85 -90

328

526

311

z =

(12) Compute the determinant of the Matrix Z?

A) B) C)

Select one of the following three options:

-70 85 -90

The answer is incorrect! Check your calculations!

Now it’s your turn

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328

526

311

z =

(12) Compute the determinant of the Matrix Z?

A) B) C)

Select one of the following three options:

-70 85 -90

Congratulations! You understood the

concept of calculating a determinant of a 3x3

matrix!