Matrix methods — order of the flexibility matrix In force (flexibility) method of analysis, the order (size) of the flexibility matrix is:

Introduction / Context:
The flexibility (force) method solves indeterminate structures by selecting redundants and enforcing compatibility through displacements. The core matrix in this approach relates generalized forces (redundants) to corresponding displacements via flexibility coefficients.

Given Data / Assumptions:

• We apply the classical force method to a statically indeterminate structure.
• Redundants are chosen, forming the unknown force vector.
• Flexibility coefficients represent displacements due to unit redundants.

Concept / Approach:
If r redundants are selected, the unknown vector has r components. The compatibility equations provide r conditions, and the flexibility matrix [f] must map an r-vector of redundants to an r-vector of displacements. Therefore, [f] is an r × r square matrix.

Step-by-Step Solution:
1) Choose r redundants → unknown force vector size = r.2) Compute flexibility coefficients f_ij = displacement at i due to unit force at j.3) Form [f] of order r × r.4) Solve [f]{R} = {Δ} for {R}, where {Δ} are required compatibility displacements.

Verification / Alternative check:
Examples for continuous beams with one redundant yield 1×1 matrices; two-span frames with two redundants produce 2×2 matrices, confirming the rule.

Why Other Options Are Wrong:
Options b, c, and d contradict the one-to-one mapping necessity between redundants and compatibility equations.

Common Pitfalls:
Over-specifying redundants; mixing stiffness and flexibility formulations; sign convention errors when assembling f_ij.

Final Answer:
equal to the number of redundant forces