Hoffman & Kunze32

Solution to Linear Algebra Hoffman & Kunze Chapter 9.2
Exercise 9.2.1 Solution: (a) No. Since $f(0,\beta)\ne 0$. (b) No. Since $f((0,0),(1,0))\ne 0$. (c) Y...
Solution to Linear Algebra Hoffman & Kunze Chapter 7.5
Exercise 7.5.1 If $N$ is a nilpotent linear operator on $V$, show that for any polynomial $f$ the se...
Solution to Linear Algebra Hoffman & Kunze Chapter 7.1
Exercise 7.1.1 Let $T$ be a linear operator on $F^2$. Prove that any non-zero vector which is not a ...
Solution to Linear Algebra Hoffman & Kunze Chapter 6.8
Exercise 6.8.3 If $V$ is the space of all polynomials of degree less than or equal to $n$ over a fie...
Solution to Linear Algebra Hoffman & Kunze Chapter 6.6
Exercise 6.6.1 Let $V$ be a finite-dimensional vector space and let $W_1$ be any subspace of $V$. Pr...
Solution to Linear Algebra Hoffman & Kunze Chapter 6.5
Exercise 6.5.1 Find an invertible real matrix $P$ such that $P^{-1}AP$ and $P^{-1}BP$ are both diago...
Solution to Linear Algebra Hoffman & Kunze Chapter 6.4
Exercise 6.4.1 Let $T$ be the linear operator on $\mathbb R^2$, the matrix of which in the standard ...
Solution to Linear Algebra Hoffman & Kunze Chapter 6.3
Exercise 6.3.1 Solution: The minimal polynomial for the identity operator is $x-1$. It annihilates t...
Solution to Linear Algebra Hoffman & Kunze Chapter 6.2
Exercise 6.2.1 In each of the following cases, let $T$ be the linear operator on $\mathbb R^2$ which...
Solution to Linear Algebra Hoffman & Kunze Chapter 5.2
Exercise 5.2.1 Each of the following expressions defines a function $D$ on the set of $3\times3$ mat...