Answer Happy

In bridge design, one is interested in connecting lightweight pieces together to make a truss which can support weight. The pieces of the truss (black lines in Figure 1) are connected together by pin joints (blue boxes) which are designed to rotate and transfer forces between the pieces. f₁ 2 F₁ f4 1-4 f₁ f4 1 3 f₂ N₁ f3 70 3, fs fs 5,000 N f3 4 F₂
4. Suppose the load of 5,000 newtons at joint 3 is replaced by the "free" (unknown) force, F3. (a) Write the system in the form Af = b where f = [ƒ1 ƒ2 ƒ3 ƒ4 ƒ5 F1 F2 F3]¹. (b) What are the orders of A, f and b? Is the system overdetermined, underdetermined or neither? (c) Is it possible to calculate the determinant of A? If so, find it. If not, explain why not. (d) Can the coefficient matrix be inverted? If so, find the inverse of matrix A. If not, explain why not. (e) Is the resulting linear system still solvable? If so, solve it. If not, explain why not. Include any matrices you use to solve the system in your report and display your solution in a table. 5. If F₁ and F₂ turn out to be negative, what does this mean physically?