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## System of the linear equation: ISI MMA 2018 Question 11

Understand the problem The value of  (lambda)  for which the system of linear equations 2x – y – z = 12 , x -2y +z = -4 , x +y + (lambda)z = 4 has no solution is  Source of the problem Sample Questions (MMA) :2019 Topic Linear Algebra Difficulty Level...

## Application of eigenvalue in degree 3 polynomial: ISI MMA 2018 Question 14

Understand the problem Let A be a 3 x 3 real matrix with all the diagoanl entries equal to 0 . If 1 + i is an eigen value of A , the determinant of A equal ? Source of the problem Sample Questions (MMA ) :2019 Topic Linear Algebra Difficulty Level Medium Suggested...

## To find Trace of a given Matrix : ISI MMA 2018 Question 13

Understand the problem If A = begin{bmatrix} 2&i\i&0end{bmatrix} , the trace of (A^{10}) is Source of the problem Sample Questions (MMA):2019 Topic Linear Algebra Difficulty Level Medium Suggested Book Introduction to Linear Algebra by Pearson Start with hints...

## Order of rings: TIFR GS 2018 Part B Problem 12

Understand the problem The number of rings of order 4, up to isomorphism, is:(a) 1(b) 2(c) 3(d) 4. Source of the problem TIFR GS 2018 Part B Problem 12 Topic Abstract Algebra Difficulty Level Easy Suggested Book Dummit and Foote Start with hints Hint 0Hint 1Hint 2Hint...

## Last three digit of the last year: TIFR GS 2018 Part B Problem 9

Understand the problem What are the last 3 digits of (2^{2017})?(a) 072(b) 472(c) 512(d) 912. Source of the problem TIFR GS 2018 Part B Problem 9 Topic Number theory Difficulty Level Easy Suggested Book Burton Start with hints Hint 0Hint 1Hint 2Hint 3 Do you really...

## Group in graphs or graphs in groups ;): TIFR GS 2018 Part A Problem 24

Understand the problem Let G be a finite group and g ∈ G an element of even order. Then wecan colour the elements of G with two colours in such a way that x andgx have different colours for each x ∈ G. Source of the problem TIFR GS 2018 Part A Problem 24 Topic...