A square matrix A is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is denoted by s(A) and is called the magic sum of the matrix A. Let V be the vector space of 2 x 2 half-magic squares. (a) Find -1 Consider the linear operator L :V → V that subtracts the magic sum from every entry in the matrix. More preciselly, L(A) := A – s(A) (b) Find -1 (c) Find an ordered basis B for V. B=( (d) Find the matrix (L]B of L in your chosen basis B.

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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.