Joshua Cook comments

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                                            Joshua Cook

gaussian elimination - struggling to understand why it's allowed or how it works

Are you struggling because he seems to ignore the right hand side of the equation?

What makes an equation linear?

I think that there will be a lot more discussion about this. We will come to define a vector space as having the following two properties: 1. closed under vector...

What makes an equation linear?

The statement in the parentheses is identical. "Closed" means that the sum of the two vectors is in the same vector space as the original two vectors. For multiplication it...

What makes an equation linear?

So I guess to say simply, "closed" means "in the same vector space".

Find two points on the line of intersection of the three planes t = 0 and z = 0 and x + y + z + t = 1 in four-dimensional space.

An intersection of 3 4-planes would be a line. The intersection of 3 3-planes would be a point. The intersection of 3 5-planes would be a 3-plane. Another way to...

Find two points on the line of intersection of the three planes t = 0 and z = 0 and x + y + z + t = 1 in four-dimensional space.

Just riffing now, but think about how a point splits R^1 in two. A line splits R^2 in two. A 3-plane (or what we normally call a plane) splits R^3...

Find two points on the line of intersection of the three planes t = 0 and z = 0 and x + y + z + t = 1 in four-dimensional space.

R^1 is just a the number line in the reals. R^2 is the traditional cartesian plane. R^3 is three space ...

homework origianl sources and solutions

I am making home works. They come from the text. IMO solutions should come from the community. I am putting my work for hw 1 up Tmrw