Problem 2
Label the following statements as true or false. Assume that all vector spaces are finite-dimensional. (a) Every linear operator T has a polynomial p(t) of largest degree for which 7->(T) = TQ. (b) Every linear operator has a unique minimal polynomial. (c) The characteristic polynomial of a linear operator divides the minimal polynomial of that operator. (d) The minimal and the characteristic polynomials of any diagonalizable operator are equal. (e) Let T be a linear operator on an n-dimensional vector space V, p(t) be the minimal polynomial of T, and f(t) be the characteristic polynomial of T. Suppose that f(t) splits. Then f(t) divides \p(t)\n - (f) The minimal polynomial of a linear operator always has the same degree as the characteristic polynomial of the operator. (g) A linear operator is diagonalizable if its minimal polynomial splits. (h) Let T be a linear operator on a vector space V such that V is a T-cyclic subspace of itself. Then the degree of the minimal polynomial of T equals dim(V). (i) Let T be a linear operator on a vector space V such that T has n distinct eigenvalues, where n dim(V). Then the degree of the minimal polynomial of T equals n.

Step-by-Step Solution:
Step 1 of 3
L6 - 7 2 x − 1 If f(x)= m sec= x − 1 ,nirheoli: x f(x) x f(x) 0.5 1.5 1.5 2.5 0.9 1.9 1.1 2.1 0.99 1.99 1.01 2.01 0.999 1.999 1.001 2.001 Notesthat f(x) a x so in our example, slope of the tangent line = m tan = x − 1 We use the notation: lfx→1 im(x)=mlx→1 =2 x − 1 Introduction to Limits Def. Let f(x)b eaufi.W eayhtl f(x)= L x→c if we can make the values of f(x)a baileo L by taking x suﬃciently close to c (on either side of c)b tnt equal to c.

This full solution covers the following key subjects: . This expansive textbook survival guide covers 43 chapters, and 881 solutions. This textbook survival guide was created for the textbook: Linear Algebra , edition: 4. Since the solution to 2 from 7.3 chapter was answered, more than 232 students have viewed the full step-by-step answer. Linear Algebra was written by and is associated to the ISBN: 9780130084514. The answer to “Label the following statements as true or false. Assume that all vector spaces are finite-dimensional. (a) Every linear operator T has a polynomial p(t) of largest degree for which 7->(T) = TQ. (b) Every linear operator has a unique minimal polynomial. (c) The characteristic polynomial of a linear operator divides the minimal polynomial of that operator. (d) The minimal and the characteristic polynomials of any diagonalizable operator are equal. (e) Let T be a linear operator on an n-dimensional vector space V, p(t) be the minimal polynomial of T, and f(t) be the characteristic polynomial of T. Suppose that f(t) splits. Then f(t) divides \p(t)\n - (f) The minimal polynomial of a linear operator always has the same degree as the characteristic polynomial of the operator. (g) A linear operator is diagonalizable if its minimal polynomial splits. (h) Let T be a linear operator on a vector space V such that V is a T-cyclic subspace of itself. Then the degree of the minimal polynomial of T equals dim(V). (i) Let T be a linear operator on a vector space V such that T has n distinct eigenvalues, where n dim(V). Then the degree of the minimal polynomial of T equals n.” is broken down into a number of easy to follow steps, and 202 words. The full step-by-step solution to problem: 2 from chapter: 7.3 was answered by , our top Math solution expert on 07/25/17, 09:33AM.