Question

From Problem 16.1 in Exercises on orthogonal vectors and subspaces:
I don't understand what this problem is asking.
First, where does the idea of "Multiply the equations x1 − x2 = 1, x2 − x3 = 1 and x1 − x3 = 1 by numbers y_1, y_2 and y_3" come from? Why is it posed?
Second, in the solution "1 + 1 − 1 = 1" is based on what kind of calculation? Thanks.
Also: I notice I can use Latex (a math language, for those who don't know) in reply posts but I can't seem to use in the original question. What do I do?

Answer 1

Hi John, which section/question number from Intro to Linear Algebra edition 4?

Answer 2

Sorry if my question is confusing. It appears many people are posting questions based on something they read in a Gilbert Strang textbook. However, my question is based on the online version of Strang's course available at the MIT OCW website. Problem 16.1 is one of the PDF homework problems from the 1st lecture in Unit 2 of the course.

Answer 3

The y's are chosen to give zero on the left hand side. If you were doing this by elimination, you would apply the same steps to the right hand side as you updated your augmented matrix, and you would discover that you're left with some nonzero entry on the RHS. The chosen values for the y's can be eyeballed or you could get them via elimination.

Answer 4

Thanks. Will get back to you later, because I'm now reviewing earlier chapters.