Question 22 - Week 3 Practice

Question 22

00:00Est. 2 min

Marks:+2.000.00

If addition and scalar multiplication on

V=\mathbb{R}^2

are defined as follows: addition:

(x_1,y_1)+(x_2,y_2)=(0,0)

for

(x_1,y_1),(x_2,y_2)\in V

; scalar multiplication:

c(x,y)=(0,0)

for

(x,y)\in V

and

c\in\mathbb{R}

. Consider the statements: 1. There exists an element

0

V

such that

0+v=v

for all

v\in V

. 2. For each

v\in V

and

a,b\in\mathbb{R}

(a+b)v=av+bv

. 3. For each scalar

a\in\mathbb{R}

and

v_1,v_2\in V

a(v_1+v_2)=av_1+av_2

. 4. 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

Easy Difficulty

16 October 2022

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