## MATHEMATICS Strategy, Booklist and Sample Answers – By Nitish K Rank – 8 and Maths Topper CSE – 2014

STRATEGY FOR MATHEMATICS OPTIONAL (UPSC CSE MAINS) Nitish K, IAS (Rank – 8, CSE – 2014)  His Blog   Who can take Mathematics as an optional? A large number of aspirants called or messaged me saying that they have decided to or wanted to take Maths and asked me to share my strategy. When …

## Mathematics-2014: Answer Writing Challenge – 9

ARCHIVES 24 September 2014 1) Discuss for all values of k the system of equations 2x+3ky+(3k+4)z=0, x+(k+4)y+(4k+2)z=0, x+2(k+1)y+(3k+4)z=0.   2) Investigate for what values of α and µ the simultaneous equations x+y+z=6,x+2y+3z=10,x+2y+αz=µ have  (i) no solution ,(ii) a unique solution, (iii) an infinite number of solutions.     3) Show that the three equations -2x+y+z=a, …

## Mathematics-2014: Answer Writing Challenge – 8

ARCHIVES 22 September 2014   MATRICES     1) Show that if a diagonal matrix is commutative with every matrix of the same order ,then it is necessarily a scalar matrix.   2) Find the possible square roots of the two rowed unit matrix I.   3) Show that the matrix B’AB is symmetric  or …

## Mathematics-2014: Answer Writing Challenge – 7

ARCHIVES 20 September 2014 1) Find all (complex) characteristic values and characteristic vectors of the following matrices: 1 1 1 (b) 1 1 1 1 1 1             0 1 1 1 1 1             0 0 1         2) Let T  be the linear operator on R3 which is represented in the standard …