A First Course in Linear Algebra

by Robert A. Beezer
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117

Title
Chapter: 6 / Q: T10 Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A
Chapter: 6 / Q: T20 Suppose that A is a square matrix. Prove that a single vector may not be an eigenvector of A for two different eigenvalues
Chapter: 6 / Q: T22 Suppose that U is a unitary matrix with eigenvalue λ. Prove that λ has modulus 1,
Chapter: 6 / Q: T30 Theorem DCP tells us that the characteristic polynomial of a square matrix of size n has degree n
Chapter: 6 / Q: T50 Theorem EIM says that if λ is an eigenvalue of the nonsingular matrix A, then 1 is an eigenvalue of A−1
Chapter: 6 / Q: c20 Consider the matrix A below. First, show that A is diagonalizable by computing the geometric multiplicities of the eigenvalues and quoting the relevant theorem
Chapter: 6 / Q: c21 Determine if the matrix A below is diagonalizable
Chapter: 6 / Q: c22 Consider the matrix A below. Find the eigenvalues of A using a calculator and use these to construct the characteristic polynomial of A,
Chapter: 6 / Q: t15 Suppose that A and B are similar matrices. Prove that A3 and B3 are similar matrices. Generalize
Chapter: 6 / Q: C25 Define the linear transformation

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