MATH 307 Study Guide - Midterm Guide: Lu Decomposition, Row And Column Vectors, Row And Column Spaces

Compute, by hand, the factorization PA = LU for the following matrices, (where L is a lower triangular matrix with entries between -1 and 1). And use the factorization to solve the linear system of equation Ax = b. A = [2 1 1 4 3 3 8 7 9], b = [2 4 10]

Consider the matrix A = [2 1 -3 6 4 0 -4 2 1]. Calculate the LU-factorization of A. Use the LU-factorization you found in (a) to solve Ax = b for times in the following two cases: b = [0 10 -1], b = [1 12 -7] What is det(A)?

??-2 Assignment 3 0 3-4 51 8. For the matrix A-2 22 02 18 4 -6 a) Find a basis for the row space of A b) Find a basis for the column space of A 1 What is the rank of A? d) Find the nullspace of A and give the nullity of A