Let V be a vector space on R of dimension 4, and T be a linear operator on V. In case that there exists a base B of V such that the matrix associated with T with respect to the base B is with a2 + b2 + c2≠0, determine if T is diagonalizable.

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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.