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?(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solutions of matrices

**Physics Forums | Science Articles, Homework Help, Discussion**