Real Analysis Answers

Solve the following linear system Ax = b of equations with partial pivoting

x-y+3z=3

2x+y+4z=7

3x+5y-2z=6

Store the multipliers and also write the pivoting vectors.

1) If ((xn,yn)) is a bounded sequence, then

((xn,yn)) has convergent subsequence.

2)((xn,yn)) is Cauchy if and only if ((xn,yn)) is convergent.

((xn,yn)) is convergent if and only if ((xn,yn)) is bounded and every convergent subsequence of ((xn,yn)) has the same limit.

((xn,yn)) is convergent if and only if ((xn,yn)) is bounded.

((xn,yn)) is said to be Cauchy if and only if both (xn) and (yn) are Cauchy sequences in R.

A function f(x) is defined for the range -2a<=x<=2a by

f(x){2a-x if -2a<=x<0

f(x){2a+x if 0<x<=2a

Sketch f(x) and state the domain and range of f(x)

13. Let b in mathbb F satisfy 0 < b < 1.

lim (n * b ^ n) = 0 [Hint: Use the Binomial Theorem