Let T be the linear operator on R 2 defined by T(x, y) = (−y, x) i. What is the matrix of T in the standard ordered basis for R 2 ? ii. What is the matrix of T in the ordered basis B = {α1, α2 }, where α1 = (1, 2) and α2 = (1, −1)? iii. Prove that for every real number c the operator (T − cI) is invertible.

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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.