Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #121 : Matrices

Perform the following matrix operation: 

Possible Answers:

Correct answer:

Explanation:

To perform the matrix operation, you must follow the formula 

.

Using the values we have, this becomes 

 

which simplified is 

Example Question #122 : Matrices

Find the determinant of the 3x3 matrix:

 

Possible Answers:

Correct answer:

Explanation:

The formula for the determinant is as follows: 

,

where 

.

Using the matrix in the problem, we get 

Example Question #123 : Matrices

What is  ?

Possible Answers:

Correct answer:

Explanation:

To find 

, we write the rows of 

 

as columns.

Hence,

 

Example Question #124 : Matrices

Find the determinant of the 3x3 matrix 

Possible Answers:

Correct answer:

Explanation:

The formula for the determinant of a 3x3 matrix  is . Using the matrix in the problem statement, we get 

Example Question #125 : Matrices

Evaluate the determinant of the matrix.

Possible Answers:

Correct answer:

Explanation:

The determinant of the  matrix

is defined as

For the matrix in this problem the determinant is

Example Question #126 : Matrices

Find the determinant of the matrix:

Possible Answers:

Correct answer:

Explanation:

To find the determinant of the matrix, we multiply across, from top left to bottom right, and then subtract the product of multiplying across from top right to bottom left:

Our answer is

 

Example Question #127 : Matrices

Find the determinant of the 2x2 matrix 

Possible Answers:

Correct answer:

Explanation:

The formula for the determinant of a 2x2 matrix  is . Using the matrix from the problem statement, we get 

Example Question #128 : Matrices

Find the determinant of the 2x2 matrix 

Possible Answers:

Correct answer:

Explanation:

The formula foe the determinant of a 2x2 matrix   is . Using the matrix from the problem statement, we get 

Example Question #129 : Matrices

Find the determinant of the given matrix:

Possible Answers:

Correct answer:

Explanation:

The determinant of the matrix is found by multiplying from top left to bottom right, and then subtracting the product from top right to bottom left (for example, the determinant of )

Our answer is

Example Question #130 : Matrices

Find the determinant of the 2x2 matrix 

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix  we use the formula for the determinant, which is . Plugging in the values from the problem statement, we find that the determinant of the matrix is 

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