# Monthly Archives: May 2010

## Linear Algebra and Its Applications, exercise 1.3.11

Exercise 1.3.11. Given the systems of equations    and    solve both systems using Gaussian elimination. Answer: We start with the first system of equations The first elimination step produces The second elimination step produces We then back-substitute, starting with … Continue reading

## Linear Algebra and Its Applications, exercise 1.3.10

Exercise 1.3.10 (very optional). Find a method for computing the quantities ac – bd and bc + ad with three multiplications instead of four. Assuming that addition were a sufficiently faster operation than multiplication, this would provide a faster way … Continue reading

## Linear Algebra and Its Applications, exercise 1.3.9

Exercise 1.3.9. State whether the following statements are true or false. (Note that without loss of generality we can assume that no row exchanges occur during the process of elimination.) (a) Given a system in u, v, etc., where the … Continue reading

## Linear Algebra and Its Applications, exercise 1.3.8

Exercise 1.3.8. Given a system of equations of order n = 600, how long would it take to solve in terms of the number of multiplication-subtractions? In seconds, on a PC capable of 8,000 operations per second? On a VAX … Continue reading

## Linear Algebra and Its Applications, exercise 1.3.7

Exercise 1.3.7. (a) Given a system of equations A, with the first two rows the same, at what point in elimination will it become clear that A is singular? Show a 3×3 example. (b) Repeat (a), but instead assume that … Continue reading