Vector space

Vector space

University

9 Qs

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Vector space

Vector space

Assessment

Quiz

Mathematics

University

Practice Problem

Hard

Created by

Jude Immaculate

Used 2+ times

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9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

1

2

3

4

2.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Let T: R2R3T:\ R^2\rightarrow R^3  be a linear transformation defined by  T(x,y)=(xy,yx,x)T\left(x,y\right)=\left(x-y,y-x,-x\right)  , then nullity of  TT  is 

 \left\{\left(1,1\right)\right\} 

  \left\{\left(0,0\right)\right\}  

 {(2,2)}\left\{\left(2,2\right)\right\}  

 {(3,3)}\left\{\left(3,3\right)\right\}  

3.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

The linear transformation T: R2R2T:\ R^2\rightarrow R^2  such that  T(1,0)=(1,1) and T(0,1)=(1,2)T\left(1,0\right)=\left(1,1\right)\ and\ T\left(0,1\right)=\left(-1,2\right)  is given by  

 T(x,y)=(xy, x+y)T\left(x,y\right)=\left(x-y,\ x+y\right)  

 T(x,y)=(x+y, x+2y)T\left(x,y\right)=\left(x+y,\ x+2y\right)  

 T(x,y)=(xy, y)T\left(x,y\right)=\left(x-y,\ y\right)  

 T\left(x,y\right)=\left(x-y,\ x+2y\right)  

4.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Is null set a vector space?

Yes

No

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is not a meaningful expression between vectors

6.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Let  VV  be a vector space over the field  FF  . Let  WW  be a subset of  VV  . Then  WW  is a subspace of  VV  over the field  FF  if  

 WW  is a vector space over the field  FF  

  x ,  y W, x+yW and xyW\forall\ x\ ,\ \ y\ \in W,\ x+y\in W\ and\ xy\in W  

  x ,  y W and cF, x+yW and cyW\forall\ x\ ,\ \ y\ \in W\ and\ c\in F,\ x+y\in W\ and\ cy\in W  

  x ,  y W and cF ,  cx+yW \forall\ x\ ,\ \ y\ \in W\ and\ c\in F\ ,\ \ cx+y\in W\   

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In a vector space V(F), (V,+) is an......

Group

Monoid

Abelian Group

None of these

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