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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

Example Question #36 : Vector Form

What is the vector form of i+2j+3k ?

Possible Answers:

$\left \langle -1,-2,3\right \rangle$

$\left \langle 1,2,3\right \rangle$

$\left \langle 1,-2,3\right \rangle$

$\left \langle -1,2,3\right \rangle$

$\left \langle -1,-2,-3\right \rangle$

Correct answer:

$\left \langle 1,2,3\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 i+2j+3k , we can derive the vector form $\left \langle 1,2,3\right \rangle$ .

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Example Question #41 : Vectors

What is the vector form of 7i-7k ?

Possible Answers:

$\left \langle 7,0,7\right \rangle$

$\left \langle 7,0,-7\right \rangle$

$\left \langle -7,0,7\right \rangle$

$\left \langle -7,0,-7\right \rangle$

$\left \langle 0,7,-7\right \rangle$

Correct answer:

$\left \langle 7,0,-7\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 7i-7k , we can derive the vector form $\left \langle 7,0,-7\right \rangle$ .

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Example Question #37 : Vector

What is the vector form of 3j+5k ?

Possible Answers:

$\left \langle 3,0,5\right \rangle$

$\left \langle 0,-3,5\right \rangle$

$\left \langle 0,3,-5\right \rangle$

$\left \langle 0,3,5\right \rangle$

$\left \langle 0,-3,-5\right \rangle$

Correct answer:

$\left \langle 0,3,5\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 3j+5k , we can derive the vector form $\left \langle 0,3,5\right \rangle$ .

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Example Question #44 : Vectors

What is the vector form of -7i+2j-5k ?

Possible Answers:

$\left \langle 7,-2,-5\right \rangle$

$\left \langle 7,-2,5\right \rangle$

$\left \langle -7,-2,-5\right \rangle$

$\left \langle -7,2,-5\right \rangle$

$\left \langle 7,2,5\right \rangle$

Correct answer:

$\left \langle -7,2,-5\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 -7i+2j-5k , we can derive the vector form $a=\left \langle -7,2,-5\right \rangle$ .

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Example Question #41 : Vector Form

What is the vector form of -j+4k ?

Possible Answers:

$\left \langle 0,1,4\right \rangle$

$\left \langle 1,0,-4\right \rangle$

$\left \langle 0,-1,4\right \rangle$

$\left \langle 0,-1,-4\right \rangle$

$\left \langle 0,1,-4\right \rangle$

Correct answer:

$\left \langle 0,-1,4\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 -j+4k , we can derive the vector form $a=\left \langle 0,-1,4\right \rangle$ .

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Example Question #42 : Vectors

What is the vector form of 2i+10j ?

Possible Answers:

$\left \langle 2,-10,0\right \rangle$

$\left \langle 2,10,0\right \rangle$

$\left \langle -2,10,0\right \rangle$

$\left \langle -2,-10,0\right \rangle$

$\left \langle 0,2,10\right \rangle$

Correct answer:

$\left \langle 2,10,0\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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+10j , we can derive the vector form $a=\left \langle 2,10,0\right \rangle$ .

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Example Question #42 : Vector Form

What is the vector form of -8i+8j-k ?

Possible Answers:

$\left \langle 8,-8,-1\right \rangle$

$\left \langle -8,8,-1\right \rangle$

$\left \langle 8,8,1\right \rangle$

$\left \langle -8,-8,1\right \rangle$

$\left \langle 8,8,-1\right \rangle$

Correct answer:

$\left \langle -8,8,-1\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 -8i+8j-k , we can derive the vector form $\left \langle -8,8,-1\right \rangle$ .

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Example Question #44 : Vector Form

What is the vector form of 7i+2j-7k ?

Possible Answers:

$\left \langle 7,-2,-7\right \rangle$

$\left \langle 7,-2,7\right \rangle$

$\left \langle 7,2,-7\right \rangle$

$\left \langle -7,-2,-7\right \rangle$

$\left \langle 7,2,7\right \rangle$

Correct answer:

$\left \langle 7,2,-7\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 7i+2j-7k , we can derive the vector form $\left \langle 7,2,-7\right \rangle$ .

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Example Question #43 : Vector Form

What is the vector form of i-10j ?

Possible Answers:

$\left \langle 1,-10,0\right \rangle$

$\left \langle 0,1,-10\right \rangle$

$\left \langle 1,10,0\right \rangle$

$\left \langle 1,0,-10\right \rangle$

$\left \langle -1,10,0\right \rangle$

Correct answer:

$\left \langle 1,-10,0\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 i-10j , we can derive the vector form $\left \langle 1,-10,0\right \rangle$ .

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Example Question #44 : Vector Form

What is the vector form of -i+9j+3k ?

Possible Answers:

$\left \langle 1,-9,-3\right \rangle$

$\left \langle -1,9,3\right \rangle$

$\left \langle -1,-9,-3\right \rangle$

$\left \langle 1,-9,3\right \rangle$

$\left \langle 1,9,-3\right \rangle$

Correct answer:

$\left \langle -1,9,3\right \rangle$

Explanation:

In order to derive the vector form, we must map the , , -coordinates 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 -i+9j+3k , we can derive the vector form $\left \langle -1,9,3\right \rangle$ .

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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 #36 : Vector Form

Example Question #41 : Vectors

Example Question #37 : Vector

Example Question #44 : Vectors

Example Question #41 : Vector Form

Example Question #42 : Vectors

Example Question #42 : Vector Form

Example Question #44 : Vector Form

Example Question #43 : Vector Form

Example Question #44 : Vector Form

All GRE Subject Test: Math Resources

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