Consider vector space V over field F. Consider set of all linear mappings from vector space V to vector space V, i.e. set L(V). Linear mappings from L(V) can be naturally added and multiplied by a scalar from F. Select all true statements. Set L(V) with given operations is a vector space. V = ker A U A(V) for every linear mapping A from L(V), because dim V = nul(A) + rk(A). Multiplication of linear mapping from L(V) by a scalar from F is again a linear mapping from L(V). Composition of two linear mappings from L(V) is again a linear mapping from L(V).

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.