Question

if V be a vector space over the field F, then a linear transformation from V into V is called.............
(a) linear operator
(b) vector
(c) vector operator
(d) none ​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If V be a vector space over the field F, then a linear transformation from V into V is called

(a) linear operator

(b) vector

(c) vector operator

(d) none

EVALUATION

Linear transformation

Let V & W be vector spaces over the same field F . A mapping T : V → W is said to be linear transformation of T satisfies below conditions :

1. T(x+y) = T(x) + T(y) for all x , y in V

2. T(cx) = cT(x) for all c in F and all x in V

Linear operator

A linear operator is a linear transformation and W = V

Thus a linear transformation T : V → V is called a linear operator on V

FINAL ANSWER

The correct option is

If V be a vector space over the field F, then a linear transformation from V into V is called

(a) linear operator

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