Free Printable Linear Algebra Midterm exam

1.

It is a group of objects called vectors, added and multiplied by numbers.

a)

Vectors in a plane

b)

Vector space

c)

Vector subspace

d)

Vectors

2.

What do we call a vector with the same magnitude and direction?

a)

Equivalent vector

b)

Similar vector

c)

Plane vector

d)

Unit vector

3.

What type of vector has the initial and terminal point equal to zero and it is a subspace of all vectors?

a)

Similar vector

b)

Zero vector

c)

Identity vector

d)

Subspace vector

4.

It is the most important property of the vector space.

a)

Associative

b)

Commutative

c)

Closure

d)

Distributive

5.

The following are properties of a vector EXCEPT ______.

a)

There exist a zero vector.

b)

Closed under vector multiplication

c)

Closed under vector addition

d)

Closed under scalar multiplication

6.

What mathematical symbol denotes the magnitude of a vector?

a)

$v⃑$

b)

$\parallel v⃑\parallel$

c)

$\parallel v\parallel$

d)

<v>

7.

What formula is to be used in finding the component form of a vector?

a)

1 $\sqrt{(}v_1^2+v_2^2)$

b)

c)

$<\frac{x}{\parallel v\parallel},\frac{y}{\parallel v\parallel}>$

d)

$xi+yj$

8.

The following are properties of a vector space EXCEPT ______.

a)

Commutative under addition and multiplication

b)

Associative under addition and multiplication

c)

There exist a zero vector

d)

There exist –1.

9.

What is the linear combination of the vector < -8,-5>?

a)

8i+5j

b)

-8i+5j

c)

-8i-5j

d)

8i-5j

10.

What is the magnitude of the vector A <1, 8>?

a)

$\sqrt[]{63}$

b)

$\sqrt[]{65}$

c)

$\sqrt[]{62}$

d)

$\sqrt[]{66}$

11.

What is the magnitude of the vector B <2, 4>?

a)

$\sqrt[]{20}$

b)

2 $\sqrt[]{5}$

c)

5 $\sqrt[]{2}$

d)

4 $\sqrt[]{5}$

12.

What is the magnitude of the vector C <8, 9>?

a)

$\sqrt[]{146}$

b)

$\sqrt[]{154}$

c)

$\sqrt[]{145}$

d)

$\sqrt[]{144}$

13.

What is the component form of the vector U which initial is (-1, -2) and has a terminal of (2, 8)?

a)

(-3, -10)

b)

(-1, -6)

c)

(3, 10)

d)

(1, 6)

14.

What is the component form of the vector V which initial is (-5, -2) and has a terminal of (-8, -6)?

a)

(3, 4)

b)

(-13, -8)

c)

(13, 8)

d)

(-3, -4)

15.

What is the component form of the vector W which initial is (8, 3) and has a terminal of (5, 3)?

a)

(3, 0)

b)

(-3, 0)

c)

(0, 3)

d)

(0, -3)

16.

Find the unit vector which the same as Vector A <1, 4>.

a)

$<\frac{1}{\sqrt[]{17}},\frac{4}{\sqrt[]{17}}>$

b)

$<\frac{4}{\sqrt[]{17}},\frac{1}{\sqrt[]{17}}>$

c)

$<\frac{-4}{\sqrt[]{17}},\frac{-1}{\sqrt[]{17}}>$

d)

$<\frac{-1}{\sqrt[]{17}},\frac{-4}{\sqrt[]{17}}>$

17.

Find the unit vector which the same as Vector B <-3, 2>.

a)

$<\frac{2}{\sqrt[]{13}},\frac{3}{\sqrt[]{13}}>$

b)

$<\frac{2}{\sqrt[]{13}},\frac{-3}{\sqrt[]{13}}>$

c)

$<\frac{-3}{\sqrt[]{13}},\frac{2}{\sqrt[]{13}}>$

d)

$<\frac{3}{\sqrt[]{13}},\frac{2}{\sqrt[]{13}}>$

18.

Find the unit vector which the same as Vector C <-1, -3>.

a)

$<\frac{3}{\sqrt[]{10}},\frac{1}{\sqrt[]{10}}>$

b)

$<\frac{-3}{\sqrt[]{10}},\frac{1}{\sqrt[]{10}}>$

c)

$<\frac{-1}{\sqrt[]{10}},\frac{-3}{\sqrt[]{10}}>$

d)

$<\frac{1}{\sqrt[]{10}},\frac{-3}{\sqrt[]{10}}>$

19.

Which of the following vector has a magnitude of 4 and the same direction as vector U = <0, 9>.

a)

<0, 12>

b)

<1, 5>

c)

<0, 4/3>

d)

<0, 2/3>

20.

Which of the following vector has a magnitude of 3 and the same direction as vector U = <1,3>.

a)

$<\frac{1}{\sqrt[]{10}},\frac{3}{\sqrt[]{10}}>$

b)

$<\frac{3}{\sqrt[]{10}},\frac{9}{\sqrt[]{10}}>$

c)

$<\frac{-1}{\sqrt[]{10}},\frac{-3}{\sqrt[]{10}}>$

d)

$<\frac{-3}{\sqrt[]{10}},\frac{-9}{\sqrt[]{10}}>$

21.

The following vector is a subset where $c_1$ and $c_2$ is an elements of $R^2$ EXCEPT____.

a)

$\left|0\ c_1\right|$

b)

$\left|2\ \ c_2\right|$

c)

$\left|c_1\ \ c_2\right|$

d)

$\left|c_1\ \ 0\right|$

22.

Which of the following vector has a magnitude of 4 and the same direction as vector U = <0,3>.

a)

<0, 1>

b)

<0, 9>

c)

<1, 5>

d)

<0, 12>

23.

The following vector is a subset EXCEPT_______.

a)

$H=\left\{c_1\ \ 0\ \ c_2\right\}:\ c_1,c_2\ element\ of\ R^3$

b)

$H=\left\{c_1\ \ 4\ \ c_1\right\}:\ c_1\ element\ of\ R^3$

c)

$H=\left\{8c_1\ \ -2c_1\ \ 3c_1\right\}:\ c_1\ element\ of\ R^3$

d)

$H=\left\{c_1\ \ c_2\ \ c_3\right\}:\ \in\ R^3:\ c_1=4c_2+c_3$

24.

Which of the following vector is a subset.

a)

$H=\left\{2c_1\ \ -1\ \ 5c_2\right\}:\ c_1,c_2\ element\ of\ R^3$

b)

$H=\left\{c_1\ \ 0\ \ c_2\right\}:\ c_1,c_2\ element\ of\ R^2$

c)

$H=\left\{2c_1\ \ 0\ \ 2c_2\right\}:\ c_1,c_2\ element\ of\ R^3$

d)

$H=\left\{c_1\ c_2\right\}:\ c_1,c_2\ element\ of\ R^3$

25.

Which of the following vector has a magnitude of -2 and the same direction as vector C = <1,3>.

a)

$<\frac{1}{\sqrt[]{10}},\frac{3}{\sqrt[]{10}}>$

b)

$<\frac{3}{\sqrt[]{10}},\frac{1}{\sqrt[]{10}}>$

c)

$<\frac{-2}{\sqrt[]{10}},\frac{3}{\sqrt[]{10}}>$

d)

$<\frac{-2}{\sqrt[]{10}},\frac{-6}{\sqrt[]{10}}>$

26.

Which of the following initial and terminal point has a component form of <3, 1>.

a)

Terminal (1, 3), Initial (4, 2)

b)

Initial (-8, -6), Terminal (-5, -5)

c)

Initial (-2,-1), Terminal (1, 4)

d)

Terminal (5,-6), Initial (-8, 7)

27.

Which of the following vector has a magnitude of 2 $\sqrt[]{5}$ .

a)

<-2, 4>

b)

<3, 8>

c)

<4, 16>

d)

<8, 2>

28.

The following vector has a magnitude of 3 EXCEPT______.

a)

<1, 3>

b)

<0, 9>

c)

<0, 3>

d)

<-1, 0>

29.

Which of the following vector has a magnitude of 7.

a)

0j+9i

b)

0i+27j

c)

9j+0i

d)

0i-49j

30.

Which of the following vector has a linear combination of -4i-8j.

a)

<-4, -8>

b)

<4, -8>

c)

<-4, 8>

d)

<4, 8>

Linear Algebra Midterm exam

Total questions: 30

Worksheet time: 51mins

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