Question

Matrix a is said to be orthogonal Matrix if Aat =0

Answer 1

Answer:

Step-by-step explanation:

Q=

⎣

⎢

⎢

⎡

​

 

a

c

b

​

 

b

a

c

​

 

c

b

a

​

 

⎦

⎥

⎥

⎤

​

 is an orthogoanal matrix.

⇒QQ

T

=I

taking modulus on both sides gives ∣Q∣=±1 -----(1)

but according to given data in Q

a

2

+b

2

+c

2

=1 and ab+bc+ca=0 ------(2)

but

∣Q∣=

∣

∣

∣

∣

∣

∣

∣

∣

​

 

a

c

b

​

 

b

a

c

​

 

c

b

a

​

 

∣

∣

∣

∣

∣

∣

∣

∣

​

=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

⇒∣Q∣=a+b+c     (from (2))

∴a+b+c=±1