Question

if xyz=m and det p=|(x,y,z)(z,x,y)(y,z,x)|,where p is an orthogonal matrix,then (15) If y=x then z=

Answer the following question:-​

Answer 1

Answer:

pm 1root/3 is a x,y,z matrix then 15

Answer 2

Answer:

We have,

∣

∣

∣

∣

∣

∣

∣

∣

1+x

1

1

1

1+y

1

1

1

1+z

∣

∣

∣

∣

∣

∣

∣

∣

=0

⇒

∣

∣

∣

∣

∣

∣

∣

∣

x

0

1

−y

y

1

0

−z

1+z

∣

∣

∣

∣

∣

∣

∣

∣

=0, use R

1

→R

1

−R

2

and R

2

→R

2

−R

3

Now expand along first row,

⇒x[y(1+z)+z]+y(0+z)=0

⇒xy(1+z)+xz+yz=0

⇒xy+yz+zx=−xyz

⇒x

−1

+y

−1

+z

−1

=−1, divide both sides by xyz