Category Archives: linear algebra

Exercise 1.2.8. We have the following system of three of equations in three unknowns: Show that the system is singular by showing that there is a combination of the three equations that produces the contradiction 0 = 1. Find a … Continue reading →

Exercise 1.2.7. Start with equation (4) from p. 8 of the text: where a solution can be found for b = (2, 5, 7) and cannot be found for b = (2, 5, 6). Find two more values of b … Continue reading →

Exercise 1.2.6. Start with equation (4) from p. 8 of the text: and assume that b = (2, 5, 7) (a value of b for which solutions can be found for u, v, and w). The text mentions two solutions, … Continue reading →

Exercise 1.2.5. The following three equations: correspond to planes in 4-space (or space-time). Find two points on the line that is the intersection of the planes represented by the equations. Answer: We substitute the values of t and z from … Continue reading →

Exercise 1.2.4. For the following three equations: sketch the lines associated with the equation and determine whether the equations have a simultaneous solution. What about if the right-hand sides of all three equations were zero? Are there other right-hand sides … Continue reading →

Exercise 1.2.3. For the following three equations (in 4-space): what is the intersection of the three planes described by the equations? If we add a fourth equation u = -1, describe the intersection of the plane associated with this equation … Continue reading →

Exercise 1.2.2. Given the system of equations solve for u, v, and w, and then use the solution to find a linear combination of column vectors that equals the vector . Answer: First, subtract the third equation from the other … Continue reading →

Recently I’ve been interested in the problem of displaying mathematics on the web, so thought I’d try out the support on wordpress.com for LaTeX (or, more correctly, ). And what better way to test it than to put my math … Continue reading →