Question

`{:A=[(1,2,2),(2,1,-2),(a,2,b)]:}` is a matrix and AAT=91, then the ordered pair (a,b) is equal to
A. (2,1)
B. (-2,-1)
C. (2,-1)
D. (-2,1)

Answer 1

Correct Answer - B
We have,
`A A^T=91`
`rArr {:[(1,2,2),(2,1,-2),(a,2,b)][(1,2,a),(2,1,2),(2,-2,b)]=[(9,0,0),(0,9,0),(0,0,9)]:}`
`rArr {:[(9,0,a+4+2b),(0,9,2a+2-2b),(a+4+2b,2a+2-2b,a^2+4+b^2)]=[(9,0,0),(0,9,0),(0,0,9)]:}`
`rArr a+4+2b=0,2a+2-2b=0and a^2+4+b^2=9`
`rArra=-2,b=-1`
`"Hence",(a,b)=(-2,-1)`