Match the following lists :

Options

A. `{:(a,b,c,d),(s,r,q,p):}`
B. `{:(a,b,c,d),(s,p,q,r):}`
C. `{:(a,b,c,d),(q,p,s,r):}`
D. `{:(a,b,c,d),(s,q,r,p):}`

Answer

C

Explanation

a. `|M_(r)|=1/(r-1)-1/r`
`lim_(n rarr oo) sum_(r=2)^(n) (1/(r-1)-1/r)`
`=lim_(n rarr oo) [(1/1-1/2)+(1/2-1/3)+...+(1/(n-1)-1/n)]`
`=1-0=1`
b. `(A+B)^(2)=A^(2)+B^(2)`
`implies AB+BA=O`
`implies AB=-BA`
`implies |AB|=|-BA|`
`implies |A||B|=-|B||A|" "` [A and B are odd orderes matrices]
`implies |B|=-|B| (|A|=2)`
`implies |B|=0`
c. `k^(2)=|C|=("det. A")^(2)=^(2) implies k=4`
d. `A^(4)=-4I implies lambda =4`