The state of stress at a point in a 2-D body, in the x-y Cartesian coordinate system,
is represented in matrix form as [σ]. The transformation matrix [Q] rotates the
coordinate system to a new x'-y' Cartesian coordinate system. Select the
CORRECT option(s) that represent(s) the state of stress in the new coordinate
system.
Options:
(A) [Q] [σ] [Q]T
(B) [Q] [σ] [Q]-1
(C) ([Q]-1)T [σ] [Q]T
(D) [Q]-1 [σ] [Q]
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.26)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Linear Algebra & Differential Equations** under *Engineering Mathematics* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Linear Algebra & Differential Equations.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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