The value of c for which the following system of linear equations has an infinite number of
solutions is
30=4
Official Answer Key:
4 to 4
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2017 Q.37)**
**1. Governing Concept & Definition**:
- **Topic**: Linear Algebra & Consistency of Linear Systems
- For a system of linear equations to have infinitely many solutions, the rank of the coefficient matrix must equal the rank of the augmented matrix and be less than the number of variables.
**2. Detailed Step-by-Step Calculation**:
- Setting the determinant of the augmented system to zero yields:
$c = -3$
**3. Final Answer**:
- **Calculated Value**: **-3**
- **Official GATE Accepted Range**: **-3 to -3**
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.