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GRE Subject Test: Math : Determinants

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Example Questions

Example Question #11 : Linear Algebra

Given the following matrix, find the determinant, if possible.

$A=\begin{bmatrix} -4&4 \\ 4&-4 \end{bmatrix}$

Possible Answers:

There is no determinant.

Correct answer:

Explanation:

Write the formula to find the determinant given a 2 by 2 matrix.

$\begin{bmatrix} a&b \\ c&d \end{bmatrix}=ad-bc$

Substituting in the given matrix we are able to find the determinant.

$\begin{bmatrix} -4&4 \\ 4&-4 \end{bmatrix}=(-4)(-4)-(4)(4)=16-16=0$

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Example Question #12 : Linear Algebra

Evaluate the determinant of the following matrix.

$\begin{bmatrix} 5& -3\\ 7& 8 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

Remember, to evaluate the determinant of a matrix use the following:

$\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

The first step would be to write the determinant of the matrix:

$\begin{vmatrix} 5& -3\\ 7&8 \end{vmatrix}$

Now we can evaluate:

$\begin{vmatrix} 5& -3\\ 7&8 \end{vmatrix}=(5)(8)- (-3)(7)=40+21=61$

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Example Question #13 : Linear Algebra

Evaluate the determinant of the following matrix.

$\begin{bmatrix} 2& 4& 3\\ 3& 0& 1\\ 1& 2& 5 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 3 x 3 matrix, we must use the following:

$\begin{vmatrix} a& b& c\\ d& e& f\\ g& h&k \end{vmatrix}=a\begin{vmatrix} e& f\\ h& k \end{vmatrix} -b\begin{vmatrix} d& f\\ g& k \end{vmatrix} + c\begin{vmatrix} d& e\\ g& h \end{vmatrix}$

The first thing we must do is write the determinant:

$\begin{vmatrix} 2& 4& 3\\ 3& 0& 1\\ 1& 2& 5 \end{vmatrix}$

Now we can proceed to evaluate the determinant

$\begin{vmatrix} 2& 4& 3\\ 3& 0& 1\\ 1& 2& 5 \end{vmatrix}=2\begin{vmatrix} 0& 1\\ 2& 5 \end{vmatrix}-4\begin{vmatrix} 3&1 \\ 1& 5\end{vmatrix}+3\begin{vmatrix} 3& 0\\ 1&2 \end{vmatrix}$

Notice that the numbers 2, 4, and 3 are being multiplied by the determinants of the 2x2 matrices so we have:

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Example Question #1 : Determinants

Find the determinant of the matrix: $\begin{vmatrix} -4 & -7 \\ 1 & 2 \end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to recall how to find the determinant of a 2*2 matrix. To find the determinant of a $2\ast2$ matrix, we need to use the equation D=ad-bc , where =Determinant, and a,b,c,d are from the matrix.

Step 2: Identify a,b,c, and d in the original matrix.
a=first number on top row, b=second number on top row (next to a), c=first number on the bottom row, and d is the second number on the bottom row (next to c).

In this matrix, a=, b=, c=, and d=.

Step 3: Substitute the values of a,b,c, and d into the equation to find the determinant of the matrix.

$ad-bc=(-4\cdot 2)-(-7\cdot 1)$ We will simplify the right side.

ad-bc=(-8)-(-7) . We see that there are two negative signs in the middle, which will become a plus sign.

ad-bc=-8+7 . Simplify the right side.

ad-bc=-1 . is the determinant.

The determinant of the matrix is .

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Example Question #2 : Determinants

Find the determinate of Matrix A.

$A=\begin{bmatrix} 8&2 \\ 5& 3 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

Matrix A is given below.

$A=\begin{bmatrix} a&b \\ c& d \end{bmatrix}$

The formula for the determinate of a 2x2 matrix is:

det(A)=ad-bc

Plugging in the values gives us:

det(A)=8*3-5*2=24-10=14

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GRE Subject Test: Math : Determinants

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #11 : Linear Algebra

Example Question #12 : Linear Algebra

Example Question #13 : Linear Algebra

Example Question #1 : Determinants

Example Question #2 : Determinants

All GRE Subject Test: Math Resources

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