Consider the vector space R' with the Euclidean inner product (l.e. the dot product). Let T:R R' be the linear operator defined by T(u) = projlu) (the orthogonal projection of u onto V). where V is a foxed vector. Which of the following statements is true? O T is one-to-one but not onto O T is an isomorphism O T is onto but not one-to-one O rank of T is 1 O nullity of T is 1

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A: The answer is given in handwritten form in the step-2 box. Please check it.

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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.