The vector space V over R has a basis {u, v, w}. The linear map o : V → R² has the property that dlu) = (: ) ; au) = ( ); olw) = ; ø(v). l; ø(w) (;). $(u) %3D %3D Describe the kernel and image of ø, compute the dimensions of these and verify that the rank-nullity cheorem holds.

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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.