Is this a valid math order?

Yes, you can do it that way. You don't need Calculus 1, 2, and 3 or even differential equations to solve Linear algebra.

Oh no. You need Calculus for Linear Algebra(except for if it's a very basic linear algebra class). Before Calculus you need Trignometry and/or Pre-Calculus after Algebra 2. Then Calculus 1, after that Calculus 2, after that Calculus 3. Then linear Algebra. At my college and most schools I know of Calculus 3 is the only Pre-Requisit to linear Algebra. But there is a specialized kind of Calculus II(Engineering Calculus II) that allows you to go into linear Algebra without Calc III. Sometimes you'd have to take college algebra before Trigonometry. And some colleges sometimes ask you to do both Trig and Pre-Calc which is kind of redundant as they're kind of the same. So in most cases it's:

arithmetic -> pre-algebra -> algebra 1 -> geometry -> algebra 2 -> trigonometry/pre-calculus -> calculus I -> calculus II -> calculus III -> linear algebra

I'm not trying to discourage you or anything. Although it doesn't sound as if this is what I'm saying, but you can take Linear Algebra after Algebra 2 because by then you'd known the basic fundamentals needed in most "high classes" like Calc. But I'm not sure of if the class you'd be taking will be exactly something that could be used as college credit.

arithmetic -> pre-algebra -> algebra 1 -> geometry -> algebra 2 -> Trigonometry -> Calculus -> Calculus 2 ->...