Question 25 - Week 3 Practice | Prasnya

Prasnya

Continue with Google

Practice path

Qualifier / Quiz 1

Go to subjectMathematics 2 Go to chapterWeek 3

Question 25

00:00Est. 3 min

Marks:+4.000.00

If addition and scalar multiplication on

V=\mathbb{R}^2

are defined by

(x_1,y_1)+(x_2,y_2)=(x_1+x_2,y_1+y_2)

and

c(x,y)=(x,cy)

, consider the statements: 1. There exists a zero vector

0\in V

such that

0+v=v

for all

v\in V

. 2. There exists a vector

v'\in V

such that

v'+v=v+v'=0

for all

v\in V

. 3. For each

v\in V

,

1v=v

. 4. For each

v\in V

and

a,b\in\mathbb{R}

,

(a+b)v=av+bv

. 5. For each

a\in\mathbb{R}

and

v_1,v_2\in V

,

a(v_1+v_2)=av_1+av_2

. 6. For each

v\in V

and

a,b\in\mathbb{R}

,

(ab)v=a(bv)

. Which statement is not true? Enter the serial number.

Integer answer

Medium Difficulty

05 June 2022

Your answer

Sign in to check answer