D. Wellington

We had our first test and I'm trying to understand what it is I'm missing. I list each of the questions below, followed by what I answered. 1. Let v1=[ 1 ] and v2 = [ 1 ] --- Find a nonzero vector w that exists in R^3 such that {v1, v2, w} is linearly independent. [ 1 ] [ 2 ] [ 1 ] [ 3 ] ans: w = [ 1 ] this was assuming that as long as the vector was a multiple of the of the vectors then the set would be linearly independent. [ 4 ] [ 6 ] 2. Find the general solution to the equation A*x = 0 (where x is a vector). Give your answer in parametric vector form. A = [ 1 2 0 -2 0 ] [ 0 0 1 2 0 ] [ 0 0 0 0 1 ] ans: this one I had no idea

Thank you for your reply ecoli and I understand [math] A^-1 [/math]; however, I don't understand why it is necessary to do so --- in other words, what is the application of [math] A^-1 [/math]? Does the elementary matrix act as a "key" that unlocks a matrix, like something you might find in cryptography? It helps me to understand the topics in mathematics if I can understand where it might apply (real-world problem). For instance, does it allow us to construct a more detailed model of whatever is being tested?

We've stepped into matrix operations this week and there are a few theorems that I don't quit understand. Now transposing a matrix is fairly straightforward and easy to comprehend, at least with small matrices. The part I'm having trouble with is the invertible matrix. I understand the key component that A^-1 is the inverse of A; however, I'm absolutely lost by the idea -- Ep...E2, E1A=In and the algebraic transformations of this equation. What is the purpose in finding the elementary matrix and what is a good way to visualize and understand this concept?

I would like to hear any advice the college-veterans might have for their younger counterparts concerning their pursuit for a college degree. What would you do differently if given the opportunity to go back to school? How would you approach your studies? Would you be more degree specific, or broaden your area of study? Would you have studied abroad? Or possibly given more of your free time to internships, or volunteer opportunities? Thank you for your replies!