SAT II Math I : Matrices

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

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Example Questions

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Example Question #1 : Matrices

Define .

Give .

Possible Answers:

 is not defined.

Correct answer:

 is not defined.

Explanation:

The inverse of a 2 x 2 matrix  , if it exists, is the matrix 

First, we need to establish that the inverse is defined, which it is if and only if determinant .

Set , and check:

The determinant is equal to 0, so  does not have an inverse.

Example Question #2 : Matrices

Give the determinant of the matrix 

Possible Answers:

Correct answer:

Explanation:

The determinant of the matrix  is 

Substitute :

Example Question #7 : Find The Sum Of Two Matrices

Simplify:

Possible Answers:

Correct answer:

Explanation:

Matrix addition is very easy! All that you need to do is add each correlative member to each other. Think of it like this:

Now, just simplify:

There is your answer!

Example Question #3 : Matrices

Simplify:

Possible Answers:

Correct answer:

Explanation:

Matrix addition is really easy—don't overthink it! All you need to do is combine the two matrices in a one-to-one manner for each index:

Then, just simplify all of those simple additions and subtractions:

Example Question #11 : Matrices

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

Example Question #2 : Matrices

Simplify:

Possible Answers:

Correct answer:

Explanation:

Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.

Example Question #85 : Sat Subject Test In Math I

What is ?

Possible Answers:

Correct answer:

Explanation:

You can begin by treating this equation just like it was:

That is, you can divide both sides by :

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore, 

Example Question #2581 : Act Math

Given the following matrices, what is the product of  and ?

 

Possible Answers:

Correct answer:

Explanation:

When subtracting matrices, you want to subtract each corresponding cell.

 

 

Now solve for  and 

 

 

Example Question #4 : Matrices

If , what is ?

 

Possible Answers:

Correct answer:

Explanation:

You can treat matrices just like you treat other members of an equation. Therefore, you can subtract the matrix

from both sides of the equation.  This gives you:

Now, matrix subtraction is simple. You merely subtract each element, matching the correlative spaces with each other:

Then, you simplify:

Therefore, 

Example Question #5 : Matrices

Simplify:

 

Possible Answers:

Correct answer:

Explanation:

The dimensions of the matrices are 2 by 2.  

The end result will also be a 2 by 2.

Evaluate the matrix.

The correct answer is: 

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