Free Printable Math Mjr 228: Quiz #3

1.

Which of the following is always included in the subspace?

a)

1

b)

0

c)

negative values

d)

positive values

2.

The following are criteria of subspace when H is in Rⁿ EXCEPT

a)

The zero vector is in H

b)

If $\overrightarrow{u}$ and $\overrightarrow{v}$ are in H, then $\overrightarrow{u}$ + $\overrightarrow{v}$ is in H

c)

If $\overrightarrow{u}$ is in H and c is in R, then c $\overrightarrow{v}$ is in H.

d)

If $\overrightarrow{u}$ + $\overrightarrow{v}$ and $\overrightarrow{u}$ $\overrightarrow{v}$ is nth unit away from the origin

3.

When a vector is not in the set under scalar multiplication, the set is not a subspace.

a)

True

b)

False

c)

Cannot be determined

4.

The zero vector in the vector space R⁴ is

a)

(0,0)

b)

(0,0,0)

c)

(0,0,0,0)

d)

none of these

5.

This picture shows a set of points in the plane $\mathbb{R}^2$ . Which of the following axioms of a vector space is NOT satised for this set?

a)

Closure under Addition

b)

Additive Identity.

c)

Additive Inverses.

d)

None of the above.

6.

Describe the location of point ( -2, 4, -5 ) in relation to the origin.

a)

Left 2, Up 4, Back 5

b)

Down 2, Right 4, Back 5

c)

Back 2, Right 4, Down 5

d)

Left 2, Right 4, Down 5

7.

What are the coordinates of the point shown in the picture.

a)

( 2, -4, 3 )

b)

( 2, -3, 3 )

c)

( 3, -4, 2 )

d)

(-3, -4, 2 )

8.

What are the coordinates of the point shown in the picture.

a)

( 0, 1, -1 )

b)

( 1, -1, 0 )

c)

( 1, 0 -1 )

d)

( 1, 1, 1 )

9.

Any span is a subspace of R^N if the vectors are in R^N

a)

True

b)

False

c)

Maybe

d)

Cannot be determined

10.

Which of the following is a subspace for R³?

a)

H={(x, y, z | 25x + 32y + 2z = 16}

b)

H={(x, y, z| x + y + z=5}

c)

H={(x, y, z| 100x - 25y + z = 0}

d)

All of the choices

11.

which of the following is a vector space?

a)

Q over R

b)

R over C

c)

Q over C

d)

R over R

12.

This is a collection of objects called vectors on which we have two operations: vector addition and scalar multiplication.

a)

Vectors

b)

Subspace

c)

Linear

d)

3D

13.

Is $\left[\left(x,\ y\right):xy\le0\right]$ a vector space?

a)

Yes

b)

No

14.

Which of the following is a vector space?

a)

Linear

b)

Polynomial

c)

Quadrants I and IV

d)

Binomials

15.

$Which\ of\ the\ following\ is\ not\ a\ subspace\ of\ R^{3\ }\left(R\right)$

a)

$\left\{\left(x,y,z\right):\ 2x+3y+4z=0\right\}$

b)

$\left\{\left(x,y,z\right):x,y,z\in Q\right\}$

c)

$\left\{\left(x,y,z\right):x=0\right\}$

d)

$\left\{\left(x,y,z\right):z=0\right\}$

16.

Is a vector space is also a subspace?

a)

True

b)

False

17.

Is a subspace is also a vector space?

a)

True

b)

False

Math Mjr 228: Quiz #3

Total questions: 17

Worksheet time: 18mins

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