A First Course in Linear Algebra

by Robert A. Beezer
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117

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Chapter: 5 / Q: M20 Construct a 3×3 nonsingular matrix and call it A
Chapter: 5 / Q: M30 Construct an example to show that the following statement is not true for all square matrices A and B of the same size: det (A + B) = det (A) + det (B)
Chapter: 5 / Q: T10 Theorem NPNT says that if the product of square matrices AB is nonsingular, then the individual matrices A and B are nonsingular also. Construct a new proof of this result making use of theorems about determinants of matrices
Chapter: 5 / Q: T15 Use Theorem DRCM to prove Theorem DZRC as a corollary. (See Proof Technique LC.)
Chapter: 5 / Q: T20 Suppose that A is a square matrix of size n and
Chapter: 5 / Q: T25 Employ Theorem DT to construct the second half of the proof of Theorem DRCM (the portion about a multiple of a column)
Chapter: 6 / Q: C10 Find the characteristic polynomial of the matrix A =
Chapter: 6 / Q: C11 Find the characteristic polynomial of the matrix A =
Chapter: 6 / Q: C12 Find the characteristic polynomial of the matrix A =
Chapter: 5 / Q: C20 Find the eigenvalues, eigenspaces, algebraic multiplicities and geometric multiplicities for the matrix below

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