Calculus 3 : Matrices

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #645 : 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 #646 : 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 #647 : Vectors And Vector Operations

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and  

The resulting matrix product is then:

Example Question #648 : Vectors And Vector Operations

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and 

The resulting matrix product is then:

Example Question #649 : Vectors And Vector Operations

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and  

The resulting matrix product is then:

Example Question #650 : Vectors And Vector Operations

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and 

The resulting matrix product is then:

Example Question #51 : Matrices

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and 

The resulting matrix product is then:

Example Question #52 : Matrices

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and 

The resulting matrix product is then:

Example Question #53 : Matrices

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and 

The resulting matrix product is then:

Example Question #54 : Matrices

Find the matrix product of , where  and  .

Possible Answers:

Correct answer:

Explanation:

In order to multiply two matrices, , the respective dimensions of each must be of the form  and  to create an  (notation is rows x columns) matrix. Unlike the multiplication of individual values, the order of the matrices does matter.

For a multiplication of the form

The resulting matrix is

The notation may be daunting but numerical examples may elucidate.

We're told that  and 

The resulting matrix product is then:

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