Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

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Example Questions

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Example Question #1 : Matrices

Calculate the determinant of Matrix .

Possible Answers:

Correct answer:

Explanation:

In order to find the determinant of , we first need to copy down the first two columns into columns 4 and 5. 

The next step is to multiply the down diagonals. 

The next step is to multiply the up diagonals.

The last step is to substract  from .

 

Example Question #2 : Matrices

Calculate the determinant of Matrix .

Possible Answers:

Correct answer:

Explanation:

In order to find the determinant of , we first need to copy down the first two columns into columns 4 and 5. 

The next step is to multiply the down diagonals. 

The next step is to multiply the up diagonals.

The last step is to substract  from .

Example Question #3 : Matrices

Calculate the determinant of .

Possible Answers:

Correct answer:

Explanation:

All we need to do is multiply the main diagonal and substract it from the off diagonal.

Example Question #4 : Matrices

Which of the following is a way to represent the computation using matrices?

Possible Answers:

None of the other answers

All of the above answers

Correct answer:

Explanation:

This choice is the only pair with a well-defined operation; the others are meaningless in terms of matrix multiplication.

 

Computing this we get

.

Which is the same as

.

 

This operation is true for (real) -dimensional vectors in general;

Example Question #5 : Matrices

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix

The determinant is thus:

Example Question #6 : Matrices

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix 

The determinant is thus:

Example Question #7 : Matrices

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix 

The determinant is thus:

Example Question #8 : Matrices

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix 

The determinant is thus:

Example Question #9 : Matrices

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix 

The determinant is thus:

Example Question #10 : Matrices

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

For the matrix 

The determinant is thus:

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