Let A= ( array ccc 0 & 2 q & r p & q & -r p & -q & r array ) . If AA ^ T = I ₃, then | p | is:

Step-by-step solution

A= [ array ccc 0 & 2 q & r p & q & -r p & -q & r array ] aligned & A A^ T = [ array ccc 0 & 2 q & r p & q & -r p & -q & r array ] [ array ccc 0 & p & p 2 q & q & -q r & -r & r array ] &= [ array ccc 4 q²+r² & 2 q²-r² & -2 q²+r² 2 q²-r² & p²+q²+r² & p²-q²-r² -2 q²+r² & p²-q²-r² & p²+q²+r² array ] aligned Given, A A^ T =I 4 q²+r²=p²+q²+r²=1 p²-3 q²=0 and r²=1-4 q² and 2 q²-r²=0 r²=2 q² array ll & p²= 1 2 , q²= 1 6 and r²= 1 3 & |p|= 1 2 array