Calculating the Determinant of a 3 by 3

Calculating the Determinant of a 3 by 3 Matrix 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. NEXT

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.

Video on Introduction to a 3 x 3 matrix Click here to watch the Introduction BACK NEXT

Now it's your turn (1) What is a 32 in the Matrix A? A= Select one of the following three options: A) B) C) 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. BACK NEXT

Now it's your turn (2) What is b 21 in the Matrix B? B= Select one of the following three options: A) B) C) 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. BACK NEXT

Now it's your turn (3) What is c 23 in the Matrix C? C= Select one of the following three options: A) BACK B) C) NEXT

Step 1: Definition of determinant and minor Click here BACK for the Definition video Part 1 NEXT

Now it's your turn (4) What is the M 12 (minor row 1, column 2 ) ? W= Select one of the following three options: A) BACK B) C) NEXT

Step 2: Applying Definition to a Matrix Click here BACK for the Definition video Part 2 NEXT

Now it's your turn (5) What is the 3 rd term in computing the Determinant W as shown below? |W|= =(-1)1+1 *w 11* + ? ? + (-1)1+2 *w 12* Select one of the following three options: A) (-1)1+3 *w 13* B) (-1)1+3 *w 13* C) (-1)2+3 *w 13* BACK NEXT

Step 3: Solving the Minor of a Matrix Click here BACK for the Definition video Part 3 NEXT

Now it's your turn (6)What is the determinant of the 2 by 2 matrix D? d 11 d 12 |D| = d 21 d 22 Select one of the following three options: A) |D|= (-1)1+1 d 11 d 22 + (-1) 1+2 d 12 d 21 B) |D|= (-1)1+2 d 11 d 21 + (-1) 1+1 d 12 d 22 C) |D|= (-1)1+3 d 11 d 22 + (-1) 1+3 d 12 d 21 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. BACK NEXT

Now it's your turn (7) What is the determinant of a 2 by 2 matrix? -1 2 G = -2 1 Select one of the following three options: A) 3 B) 5 C) -5 BACK NEXT

Step 4: Final Step in Computing Determinant of a Matrix Click here BACK for the Definition video Part 4 NEXT

Applying the Concept to Solving a Numerical Problem Step 1: First term of summation and Identifying the Minor Click here BACK for the Example video Part 1 NEXT

Now it's your turn (8) What is M 32 (minor 3, 2 ) in the Matrix A? A= Select one of the following three options: A) B) C) 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. BACK NEXT

Now it's your turn (9) What is M 21 (minor row 2, column 1 ) in the Matrix B? B= Select one of the following three options: A) B) C) 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. BACK NEXT

Now it's your turn (10) What is M 23 (minor row 2, column 3 ) in the Matrix C? C= Select one of the following three options: A) BACK B) C) NEXT

Applying the Concept to Solving a Numerical Problem Step 2: Writing the Summation Equation Click here BACK for the Example video Part 2 NEXT

Now it's your turn (11) What is the 3 rd term of summation of the determinant of W? IWI = = (-1)1+1*(2)* + (-1)1+2*(-4)* +? Select one of the following three options: A) (-1)1+3 *(1)* B) (-1)1+3 *(1)* C) (-1)2+3 *(1)* BACK NEXT

Applying the Concept to Solving a Numerical Problem Step 3: Final solution Click here BACK for the Example video Part 3 NEXT

Now it’s your turn (12) Compute the determinant of the Matrix Z? z= Select one of the following three options: A) -70 BACK B) 85 C) -90

Now it’s your turn (12) Compute the determinant of the Matrix Z? z= The answer is incorrect! C) -90 A) -70 B) 85 Check your calculations! Select one of the following three options: BACK

(12) Compute the determinant of the Matrix Z? Congratulations! z You understood the concept of calculating a determinant of a. C)3 x 3 -90 A) -70 B) 85 matrix! = Select one of the following three options: