Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #141 : Matrices

Evaluate the matrix operation 

Possible Answers:

Correct answer:

Explanation:

To find the sum of 2 2x2 matrices, we use the formula:

Applying to the matrices from the problem statement, we get:

Example Question #142 : Matrices

Find the determinant of the 2x2 matrix given: 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix , we use the formula:

Using the vector from the problem statement, we get:

Example Question #143 : Matrices

Find the determinant of the matrix:

Possible Answers:

Correct answer:

Explanation:

The determinant of a two-by-two matrix is given by

(The process is similar to the finding the cross product using a three-by-three matrix, where one moves from top left to bottom right, and then subtracts the result of moving from top right to bottom left). 

Our final answer is .

Example Question #144 : Matrices

Find the determinant of the 3x3 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 3x3 matrix , we use the formula

Using the matrix from the problem statement, we get

Example Question #2741 : Calculus 3

Find the determinant of the 2x2 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix ,

we use the formula

Using the matrix from the problem statement, we get 

Example Question #2742 : Calculus 3

Find the determinant of the 2x2 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix ,

we use the formula

Using the matrix from the problem statement, we get 

Example Question #741 : Vectors And Vector Operations

Find the determinant of the 3x3 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 3x3 matrix , we use the formula

Using the matrix from the problem statement and applying, we get

 

Example Question #742 : Vectors And Vector Operations

Find the determinant of the 3x3 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 3x3 matrix , we use the formula

Using the matrix from the problem statement and applying, we get

Example Question #743 : Vectors And Vector Operations

Find the determinant of the 2x2 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix  we use the definition:

Applying to the matrix from the problem statement, we get

Example Question #744 : Vectors And Vector Operations

Find the determinant of the 2x2 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix , we apply the definition:

Using the matrix from the problem statement, we get

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