SAT II Math II : Matrices

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

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Example Question #1 : Matrices

Multiply:

Possible Answers:

Correct answer:

Explanation:

The product of a 2 x 2 matrix and a 2 x 1 matrix is a 2 x 1 matrix.

Multiply each row in the first matrix by the column matrix by multiplying elements in corresponding positions, then adding the products, as follows:

\

Example Question #2 : Matrices

Multiply:

Possible Answers:

Correct answer:

Explanation:

The product of a 2 x 2 matrix and a 2 x 1 matrix is a 2 x 1 matrix.

Multiply each row in the first matrix by the column matrix by multiplying elements in corresponding positions, then adding the products, as follows:

Example Question #3 : Matrices

Define matrix  

For which of the following matrix values of  is the expression  defined?

Possible Answers:

The expression  is defined for all of the values of  given in the other responses.

Correct answer:

Explanation:

For the matrix product  to be defined, itis necessary and sufficent for the number of columns in  to be equal to the number of rows in 

 has two columns. Of the choices, only

 

 has two rows, making it the correct choice.

Example Question #4 : Matrices

Calculate: 

Possible Answers:

Correct answer:

Explanation:

To subtract two matrices, subtract the elements in corresponding positions:

 

Example Question #81 : Mathematical Relationships

Evaluate:

Possible Answers:

Correct answer:

Explanation:

The determinant of the matrix  is 

Substitute :

Example Question #82 : Mathematical Relationships

Give the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of the matrix  is 

Substitute :

Example Question #7 : Matrices

Multiply:

Possible Answers:

Correct answer:

Explanation:

The product of a 2 x 2 matrix and a 2 x 1 matrix is a 2 x 1 matrix.

Multiply each row in the first matrix by the column matrix by multiplying elements in corresponding positions, then adding the products, as follows:

Example Question #8 : Matrices

Let .

Give .

Possible Answers:

 is not defined.

Correct answer:

 is not defined.

Explanation:

 has three rows and two columns; since the number of rows is not equal to the number of columns,  is not a square matrix, and, therefore, it does not have an inverse.

Example Question #9 : Matrices

Define matrix  .

For which of the following matrix values of  is the expression  defined?

I: 

 

II: 

 

III: 

Possible Answers:

I and II only

I and III only

I only

I, II, and III

II and II only

Correct answer:

I only

Explanation:

For the matrix sum  to be defined, it is necessary and sufficent for  and  to have the same number of rows and the same number of columns.  has three rows and two columns; of the three choices, only (I) has the same dimensions.

Example Question #1 : Matrices

Let  and  be the 2 x 2 identity matrix. 

Let .

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

The 2 x 2 identity matrix is  .

 

, or, equivalently,

,

so

Subtract the elements in the corresponding positions:

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