Sure, it is does not require the knowledge of linear algebra, but the subtopic of vector algebra.
You need to understand inner products (or dot product), and vectorial product (or cross product). The concept of determinant may help for the vectorial product, but you can also memorize a technique such as Cofactors or Sarrus rule.
All vectors in Statics are either in the plane (2 components) or in the space (3 components).
You should be fine. Just make sure you understand the basics right away.
I'll outline them again here.
Math Prereqs
1) Concept of Vector, and the algebra of Vectors. This includes the products, the norm or modulus of a vector, and how to normalize a vector (find unit vector along the direction of a vector)
2) Solving Simultaneous Equations, You may use Cramer's method or substitution, elimination or other methods.
Physics Concepts
3) Radius Vector or R - vector, Force Vectors, and Moment Vectors (This are usually represented by Double Arrows, and are normal to the surface where they act). Remember that also with moments and forces comes the convention of signs (which direction is positive and which is negative). Do note that moments are also called Couples in Statics.
4) The Static Equilibrium Equations. Sum of Forces, and Sum of Moments must be zero. Also, for forces partition, remember Newton's third law. Thus if you have a rigid body and you unhinge the forces on the separate FDB must be included in opposite directions.
Static Outline
5) The Line of Action principle for Force Vectors. You can slide the Force vector along its line of action without changing its effect on a rigid body (Note that this is not true in deformable bodies such as those you learn in Mechanics/Strength of Materials). Also, Moments are free vectors and can move to any points within the plane they act, as long as they are still normal to the plane. This is important to remember, many students completely ignore these basic principles.
6) Any system of Statics can be turned into a Resultant Force-Couple System. Thus, the whole idea of static is based that the resultant Force-Couple system is null. This is the transport-couple theorem. You can move a Force to any point outside of its line of action by introducing a couple to cancel the force moment effect.
7) The Parallel Axis Theorem or Steiner's 2nd Thm is useful for calculating Area Moments of Inertia. Do note that the definition of the moments to find centroids and inertia are important concepts to learn. This may require you to brush up on your Integral Calculus.
*8) If you put together these concepts, you can now know why a Truss if the forces apply on the nodes, it is assumed that the forces along the members must be acting on the same line of action. This is the 2 forces acting on a rigid body special equilibrium conditions. For the case of 3 forces, The forces must be concurrent. Look up Varignon's Thm. For rigid bodies connected with hinges, this is the principle where the solution method is derived along with Newton's 3rd Law.
Another last chapter I believe is moment with respect to an axis represent by a unit vector along the axis. Probably, there are other interesting chapters. However, I think it is best you are surprised by the course. Statics is one of my favorite courses along with Mechanics of Materials and Structural Mechanics while I was an undergrad.
