Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #601 : 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 #602 : 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 #603 : 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 #604 : 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:

Note that the zero-value determinant means that the two columns are not lineraly independent; one can be found by multiplying the other by some value: in this case, the second column is one half of the first.

Example Question #605 : 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 #606 : 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 #11 : 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 #12 : 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 #13 : 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 #14 : 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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