Exercises on solving Ax = b and row reduced form R
Problem 8.1: (3.4 #13.(a,b,d) Introduction to Linear Algebra: Strang) Explain why these are all false:
a) The complete solution is any linear combination of xp and xn.
b) The system Ax = b has at most one particular solution.
c) If A is invertible there is no solution xn in the nullspace.
Problem 8.2: (3.4 #28.) Let
U and c .
Use Gauss-Jordan elimination to reduce the matrices [U 0] and [U c] to [R 0] and [R d]. Solve Rx = 0 and Rx = d.
Check your work by plugging your values into the equations Ux = 0 and Ux = c.
Problem 8.3: (3.4 #36.) Suppose Ax = b and Cx = b have the same (complete) solutions for every b. Is it true that A = C?
