Question

‘If x < y, then ax < ay for any value of a.’
Find a counter example to disprove this statement.

Answer 1

Answer:

Given the system of the equation can be written as AX=O

where A=  

⎣

⎢

⎢

⎡

​

 

1

0

a

​

 

a

1

0

​

 

0

a

1

​

 

⎦

⎥

⎥

⎤

​

, X=  

⎣

⎢

⎢

⎡

​

 

x

y

z

​

 

⎦

⎥

⎥

⎤

​

,O=  

⎣

⎢

⎢

⎡

​

 

0

0

0

​

 

⎦

⎥

⎥

⎤

​

 

For infinitely many solutions  

D=0

⇒  

∣

∣

∣

∣

∣

∣

∣

∣

​

 

1

0

a

​

 

a

1

0

​

 

0

a

1

​

 

∣

∣

∣

∣

∣

∣

∣

∣

​

=0

⇒a  

3

+1=0

⇒a  

3

=−1

⇒a=−1