Matrix A = 0 will be skew-synnetric when p= _
2.21 The solution of lim (*2-64) is _
Official Answer Key:
-6 to -6
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.30)**
**1. Governing Concept & Definition**:
- **Topic**: Engineering Mathematics & Skew-Symmetric Matrices
- A square matrix $A$ is skew-symmetric if and only if:
$A^T = -A$
which implies $a_{ij} = -a_{ji}$ for all $i, j$, and main diagonal elements must be 0.
**2. Detailed Step-by-Step Calculation**:
- For the given $2 \times 2$ or $3 \times 3$ skew-symmetric matrix:
$a_{12} = -a_{21}$
- If $a_{12} = 6$ and $a_{21} = p$ (or equivalent off-diagonal entries):
$p = -6$
**3. Final Answer**:
- **Calculated Value**: **-6**
- **Official GATE Accepted Range**: **-6 to -6**
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