Label the following statements as true or false. Assume that the underlying inner product spaces are finite-dimensional. (a) Every linear operator has an adjoint. (b) Every linear operator on V has the form x →><x, y>for some y ∈V. (c) For every linear operator T on V and every ordered basis βfor V, we have [T∗]β= ([T]β)*. (d) The adjoint of a linear operator is unique. (e) For any linear operators T and U and scalars a and b, (aT + bU)∗= aT ∗+ bU∗ . (f) For any n ×n matrix A, we have (LA)∗= LA∗.(g) For any linear operator T, we have (T∗)∗= T.

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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.