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## Average Determinant: TIFR GS 2017 Part A Problem 8.

Understand the problem True or False? Let $$n \geq 2$$ be a natural number. Let $$S$$ be the set of all $$n \times n$$ real matrices whose entries are only $$0,1$$ or $$2$$. Then the average determinant of a matrix in $$S$$ is greater than or equal to 1. Source of the...

## Spanning set of a matrix space: TIFR GS 2019, Part B Problem 6

Understand the problem True or false? For any , there exists a $latex n times n$ real matrix $latex A$ such that the set $latex {A^p mid p ≥ 1}$ spans the $latex Bbb R$-vector space $latex M_n(Bbb R)$. Source of the problem TIFR GS 2019, Part B Problem 6 Topic...

## ABC of rank: TIFR GS 2019, Part B Problem 5

Understand the problem Suppose are real matrices with .Then . We have to find out whether the statement is true or false. Source of the problem TIFR GS 2019, Part B Problem 5 Topic Linear Algebra Difficulty Level Medium Suggested Book Linear algebra, Friedberg, Insel...

## Continuous map on countable space: TIFR GS 2019, Part B Problem 3

Understand the problem >True or false: Let . Suppose each continuous function is bounded. Then is finite. Source of the problem TIFR GS 2019, Part B Problem 3 Topic General topology Difficulty Level Medium Suggested Book Topology, Munkres Start with hints Hint...

## Invertible Matrix implies identity?: TIFR GS 2019, Part B Problem 4

Understand the problem Is it possible to have a non-identity diagonalizable, invertible, complex matrix s.t characteristics polynomials of and are the same? Source of the problem TIFR GS 2019, Part B Problem 4 Topic Linear algebra Difficulty Level Hard Suggested Book...

## Invertible Matrix: TIFR GS 2019, Part B Problem 2

Understand the problem True or False: Let satisfies , then is invertible. Source of the problem TIFR GS 2019, Part A Problem 2 Topic Linear Algebra Difficulty Level Easy Suggested Book Linear Algebra: Hoffman and Kunze Start with hints Hint 0Hint 1Hint 2 Do you really...