Simplifying UPSC IAS Preparation
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 …
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, …
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ARCHIVES 23 September 2014 1) Show that every square matrix is uniquely expressible as the sum of a symmetric and a skew-symmetric matrix. 2) If A is a square matrix of order n, prove that | Adj (Adj A) | =|A|(n-1)ᴧ2 3) Find the rank of the matrix 2 -2 0 …
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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 …
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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 …
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