# Let’s Try A Warm Up MCQ

# Understand the problem

Consider the vector space V over of the polynomial functions of degree less than or equal to 3 defined on . Let defined by $latex (Tf)(x) = f(x)-xf'(x). Then the rank of T is (a) 1 (b) 2 (c) 3 (d) 4

##### Source of the problem

IIT JAM 2018 Problem 9

##### Topic

Vector Space

##### Difficulty Level

Easy

##### Suggested Book

Abstract Algebra By S.K Mapa

# Start with hints

Do you really need a hint? Try it first!

Rank(T) = dim(Range(T)) There is one easy way to calculate rank of every linear transformation. Step 1: Take by basis of the vector space . Step 2: Write down the matrix Step 3: Calculate the rank of the matrix Now can you follow these steps to get the answer?

Standard Basis of is ; ; ; So, Hence the rank is

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