Read the following statements related to the matrix analysis of structures and choose the correct option.

1. The flexibility matrix is a square matrix of order n, where n is the number of coordinates chosen for the solution of the problem at hand.

2. Due to the implementation of the Maxwell's reciprocal theorem, the flexibility matrix becomes a symmetrical matrix.

3. If the structure is unstable internally or externally, then the flexibility matrix will be a unit matrix for the given structure.

Explanation:

Matrix Analysis of Structures

Matrix analysis of structures is a method used to analyze and solve structural problems using matrices. It involves representing the structure's behavior in matrix form, which simplifies the calculation and understanding of complex structural systems. Let's analyze the given statements regarding the flexibility matrix:

• Statement 1: The flexibility matrix is a square matrix of order n, where n is the number of coordinates chosen for the solution of the problem at hand.

• Statement 2: Due to the implementation of the Maxwell's reciprocal theorem, the flexibility matrix becomes a symmetrical matrix.

• Statement 3: If the structure is unstable internally or externally, then the flexibility matrix will be a unit matrix for the given structure.

Analyzing the Given Options

1. Statement 1: This statement is correct. The flexibility matrix is indeed a square matrix of order n, where n represents the number of independent coordinates required to describe the deformation of the structure.

2. Statement 2: This statement is also correct. According to Maxwell's reciprocal theorem, the flexibility matrix is symmetric, meaning F_ij = F_ji. This property holds true for linear elastic structures.

3. Statement 3: This statement is incorrect. If the structure is unstable, the flexibility matrix will not be a unit matrix. Instead, it will not have a proper solution because the system of equations representing the structure's equilibrium will be inconsistent or singular.

Conclusion: Based on the analysis, the correct answer is:

Option 3: Statements 1 and 2 are correct, and statement 3 is incorrect.