Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #41 : Matrices

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix 

The determinant is thus:

Example Question #632 : Vectors And Vector Operations

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix 

The determinant is thus:

Example Question #633 : Vectors And Vector Operations

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix 

The determinant is thus:

Example Question #634 : Vectors And Vector Operations

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix 

The determinant is thus:

Example Question #635 : Vectors And Vector Operations

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix 

The determinant is thus:

Example Question #636 : Vectors And Vector Operations

Find the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

For the matrix 

The determinant is thus:

Example Question #641 : Vectors And Vector Operations

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 #642 : Vectors And Vector Operations

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 #643 : Vectors And Vector Operations

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:

This result is due to the columns being linearly dependent, i.e. multiples of each other. The first column is three times the second column.

Example Question #644 : Vectors And Vector Operations

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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