Problem 1E: Elementary Matrices In Exercises 1-8, determine whether the matrix is elementary. If it is, state... Problem 2E: Elementary Matrices In Exercises 1-8, determine whether the matrix is elementary. If it is, state... Problem 3E Problem 4E Problem 5E: Elementary Matrices In Exercises 1-8, determine whether the matrix is elementary. If it is, state... Problem 6E: Elementary Matrices In Exercises 1-8, determine whether the matrix is elementary. If it is, state... Problem 7E: Elementary Matrices In Exercises 1-8, determine whether the matrix is elementary. If it is, state... Problem 8E: Elementary Matrices In Exercises 1-8, determine whether the matrix is elementary. If it is, state... Problem 9E: Finding an Elementary Matrix In Exercises 9-12, let A, B, and C be A=12-3012-120, B=-12001212-3, and... Problem 10E: Finding an Elementary Matrix In Exercises 9-12, let A, B, and C be A=12-3012-120, B=-12001212-3, and... Problem 11E: Finding an Elementary Matrix In Exercises 9-12, let A, B, and C be A=12-3012-120, B=-12001212-3, and... Problem 12E: Finding an Elementary Matrix In Exercises 9-12, let A, B, and C be A=12-3012-120, B=-12001212-3, and... Problem 13E: Finding a Sequence of Elementary Matrices In Exercises 13-18, find a sequence of elementary matrices... Problem 14E: Finding a Sequence of Elementary Matrices In Exercises 13-18, find a sequence of elementary matrices... Problem 15E: Finding a Sequence of Elementary Matrices In Exercises 13-18, find a sequence of elementary matrices... Problem 16E: Finding a Sequence of Elementary Matrices In Exercises 13-18, find a sequence of elementary matrices... Problem 17E: Finding a Sequence of Elementary Matrices In Exercises 13-18, find a sequence of elementary matrices... Problem 18E: Finding a Sequence of Elementary Matrices In Exercises 13-18, find a sequence of elementary matrices... Problem 19E: Finding the Inverse of an Elementary Matrix In Exercises 19-24, find the inverse of the elementary... Problem 20E: Finding the Inverse of an Elementary Matrix In Exercises 19-24, find the inverse of the elementary... Problem 21E: Finding the Inverse of an Elementary Matrix In Exercises 19-24, find the inverse of the elementary... Problem 22E: Finding the Inverse of an Elementary Matrix In Exercises 19-24, find the inverse of the elementary... Problem 23E: Finding the Inverse of an Elementary Matrix In Exercises 19-24, find the inverse of the elementary... Problem 24E: Finding the Inverse of an Elementary Matrix In Exercises 19-24, find the inverse of the elementary... Problem 25E: Finding the Inverse of a Matrix In Exercises 25-28, find the inverse of the matrix using elementary... Problem 26E: Finding the Inverse of a Matrix In Exercises 25-28, find the inverse of the matrix using elementary... Problem 27E: Finding the Inverse of a Matrix In Exercises 25-28, find the inverse of the matrix using elementary... Problem 28E: Finding the Inverse of a Matrix In Exercises 25-28, find the inverse of the matrix using elementary... Problem 29E: Finding a Sequence of Elementary Matrices In Exercises 29-36, find a sequence of elementary matrices... Problem 30E: Finding a Sequence of Elementary Matrices In Exercises 29-36, find a sequence of elementary matrices... Problem 31E: Finding a Sequence of Elementary Matrices In Exercises 29-36, find a sequence of elementary matrices... Problem 32E: Finding a Sequence of Elementary Matrices In Exercises 29-36, find a sequence of elementary matrices... Problem 33E: Finding a Sequence of Elementary Matrices In Exercises 29-36, find a sequence of elementary matrices... Problem 34E: Finding a Sequence of Elementary Matrices In Exercises 29-36, find a sequence of elementary matrices... Problem 35E: Finding a Sequence of Elementary Matrices In Exercises 29-36, find a sequence of elementary matrices... Problem 36E Problem 37E: Writing Is the product of two elementary matrices always elementary? Explain. Problem 38E Problem 39E: Use elementary matrices to find the inverse of A=100010abc, c0. Problem 40E: Use elementary matrices to find the inverse of A=1a0010001100b1000110001000c, c0. Problem 41E: True or False? In Exercises 41 and 42, determine whether each statement is true or false. If a... Problem 42E: True or False? In Exercises 41 and 42, determine whether each statement is true or false. If a... Problem 43E: Finding an LU-Factorization of a Matrix In Exercises 43-46, find an LU-factorization of the matrix.... Problem 44E Problem 45E: Finding an LU-Factorization of a Matrix In Exercises 43-46, find an LU-factorization of the matrix.... Problem 46E: Finding an LU-Factorization of a Matrix In Exercises 43-46, find an LU-factorization of the matrix.... Problem 47E: Solving a Linear System Using LU-Factorization In Exercises 47 and 48, use an LU-factorization of... Problem 48E Problem 49E: Idempotent Matrices In Exercises 49-52, determine whether the matrix is idempotent. A square matrix... Problem 50E: Idempotent Matrices In Exercises 49-52, determine whether the matrix is idempotent. A square matrix... Problem 51E: Idempotent Matrices In Exercises 49-52, determine whether the matrix is idempotent. A square matrix... Problem 52E: Idempotent Matrices In Exercises 49-52, determine whether the matrix is idempotent. A square matrix... Problem 53E Problem 54E: Guided Proof Prove that A is idempotent if and only if AT is idempotent. Getting Started: The phrase... Problem 55E: Proof Prove that if A is an nn matrix that is idempotent and invertible, then A=In. Problem 56E: Proof Prove that if A and B are idempotent and AB=BA, then AB is idempotent. Problem 57E: Guided Proof Prove that if A is row-equivalent to B, and B is row-equivalent to C, A is... Problem 58E: Proof Prove that if A is row-equivalent to B, then B is row-equivalent to A. Problem 59E: Proof Let A be a nonsingular matrix. Prove that if B is row-equivalent to A, then B is also... Problem 60E: CAPSTONE a Explain how to find an elementary matrix. b Explain how to use elementary matrices to... Problem 61E: Show that the matrix below does not have an LU factorization. A=0110 format_list_bulleted