I'm trying to learn linear algebra by myself from a book called "Introduction to linear algebra" by A.D. Martin and V.J. Mizel. One point I'm so far pretty confused about is whether a matix has a solution only if m equals n? I think the book says that if m < n the matrix has infinite solutions, which makes sense, but it doesn't say anything about when m > n. In that case, is there a solution?

The book has problems for you to solve, but no answers. That doesn't matter if a matrix has a solution you can verify, but I'm getting a suspicious number of matrices that have no solutions. I think I don't understand the Gaussian reduction algorithm well enough, at least I find that the following matrix has no solutions, when according to the book it should since m = n.

I'll write it as an equation, I have no idea how to do it properly in latex.

2x + 3y + z = 5

x + 0y - z = 1

2x - 9y - 11z = -5

The book has problems for you to solve, but no answers. That doesn't matter if a matrix has a solution you can verify, but I'm getting a suspicious number of matrices that have no solutions. I think I don't understand the Gaussian reduction algorithm well enough, at least I find that the following matrix has no solutions, when according to the book it should since m = n.

I'll write it as an equation, I have no idea how to do it properly in latex.

2x + 3y + z = 5

x + 0y - z = 1

2x - 9y - 11z = -5

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