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GRE Subject Test: Math : Linear Algebra

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

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All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #11 : Vector

What is the vector form of 5i-2j+9k ?

Possible Answers:

$\left \langle 9,-2,5\right \rangle$

$\left \langle 5,-2,9\right \rangle$

$\left \langle 5,9,-2\right \rangle$

$\left \langle -2,5,9\right \rangle$

None of the above

Correct answer:

$\left \langle 5,-2,9\right \rangle$

Explanation:

Given 5i-2j+9k , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of 5i-2j+9k is

$\left \langle 5,-2,9\right \rangle$ .

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Example Question #22 : Vectors

What is the vector form of 2i-k ?

Possible Answers:

$\left \langle -1,2, 0\right \rangle$

$\left \langle 0,-1,2\right \rangle$

$\left \langle 2,-1, 0\right \rangle$

None of the above

$\left \langle 2,0,-1\right \rangle$

Correct answer:

$\left \langle 2,0,-1\right \rangle$

Explanation:

Given 2i-k , we need to map the , , and coefficients back to their corresponding , , and -coordinates.

Thus the vector form of 2i-k is

$\left \langle 2,0,-1\right \rangle$ .

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Example Question #23 : Vectors

What is the dot product of $a=\left \langle 7,-7,0\right \rangle$ and $b=\left \langle 2, -1,8\right \rangle$ ?

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given $a=\left \langle 7,-7,0\right \rangle$ and $b=\left \langle 2, -1,8\right \rangle$ , then:

$\left \langle 7,-7,0\right \rangle\times \left \langle 2, -1,8\right \rangle$

$=(7\times 2)+(-7\times -1)+(0\times 2)$

=14+7+0

=21

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Example Question #24 : Vectors

What is the dot product of $a=\left \langle 4,1,-1\right \rangle$ and $b=\left \langle 2, -1,8\right \rangle$ ?

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given $a=\left \langle 4,1,-1\right \rangle$ and $b=\left \langle 2, -1,8\right \rangle$ , then:

$\left \langle 4,1,-1\right \rangle\times \left \langle 2, -1,8\right \rangle$

$=(4\times 2)+(1\times -1)+(-1\times 8)$

=8+(-1)+(-8)

=-1

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Example Question #25 : Vectors

What is the dot product of $a=\left \langle 3,0,-9\right \rangle$ and $b=\left \langle -9, 2,-3\right \rangle$ ?

Possible Answers:

Correct answer:

Explanation:

The dot product of two vectors is the sum of the products of the vectors' corresponding elements. Given $a=\left \langle 3,0,-9\right \rangle$ and $b=\left \langle -9, 2,-3\right \rangle$ , then:

$\left \langle 3,0,-9\right \rangle\times \left \langle -9, 2,-3\right \rangle$

$=(3\times -9)+(0\times 2)+(-9\times -3)$

=(-27)+0+27

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Example Question #26 : Vectors

What is the vector form of $a=\left \langle 3,-2,7\right \rangle$ ?

Possible Answers:

3i-2j-7k

-3i-2j-7k

3i-2j+7k

3i+2j-7k

3i+2j+7k

Correct answer:

3i-2j+7k

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ , the vector form is $a_{1}i+a_{2}j+a_{3}k$ .

So for $a=\left \langle 3,-2,7\right \rangle$ , we can derive the vector form 3i-2j+7k .

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Example Question #21 : Vector Form

What is the vector form of $a=\left \langle -1,9,3\right \rangle$ ?

Possible Answers:

-i+9j+3k

-i-9j+3k

-i-9j-3k

i-9j+3k

i+9j+3k

Correct answer:

-i+9j+3k

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ , the vector form is $a_{1}i+a_{2}j+a_{3}k$ .

So for $a=\left \langle -1,9,3\right \rangle$ , we can derive the vector form -i+9j+3k .

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Example Question #21 : Vector Form

What is the vector form of $a=\left \langle 0,2,5\right \rangle$ ?

Possible Answers:

2i+5k

None of the above

2i+5j

2j+5k

5i+2j

Correct answer:

2j+5k

Explanation:

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ , the vector form is $a_{1}i+a_{2}j+a_{3}k$ .

So for $a=\left \langle 0,2,5\right \rangle$ , we can derive the vector form 2j+5k .

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Example Question #29 : Vectors

What is the vector form of 5i-6j+7k ?

Possible Answers:

$\left \langle 5,6,7\right \rangle$

$\left \langle -5,-6,-7\right \rangle$

$\left \langle 5,6,-7\right \rangle$

$\left \langle 5,-6,7\right \rangle$

$\left \langle 5,-6,-7\right \rangle$

Correct answer:

$\left \langle 5,-6,7\right \rangle$

Explanation:

In order to derive the vector form, we must map the vector elements to their corresponding , , and coefficients. That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ . So for 5i-6j+7k , we can derive the vector form $\left \langle 5,-6,7\right \rangle$ .

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Example Question #30 : Vectors

What is the vector form of -2i+9j ?

Possible Answers:

$\left \langle 0,-2,9\right \rangle$

$\left \langle -2,9,0\right \rangle$

$\left \langle-2, 0, 9\right \rangle$

None of the above

$\left \langle9, 0,-2\right \rangle$

Correct answer:

$\left \langle -2,9,0\right \rangle$

Explanation:

In order to derive the vector form, we must map the vector elements to their corresponding , , and coefficients. That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ . So for -2i+9j , we can derive the vector form $\left \langle -2,9,0\right \rangle$ .

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GRE Subject Test: Math : Linear Algebra

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #11 : Vector

Example Question #22 : Vectors

Example Question #23 : Vectors

Example Question #24 : Vectors

Example Question #25 : Vectors

Example Question #26 : Vectors

Example Question #21 : Vector Form

Example Question #21 : Vector Form

Example Question #29 : Vectors

Example Question #30 : Vectors

All GRE Subject Test: Math Resources

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