Question:
If $|\begin{matrix}1& 0& 0\\ x& x+2& 0\\ x^{2}& x& x+3\end{matrix}|=0$, then values of $x$ are ________.
If $|\begin{matrix}1& 0& 0\\ x& x+2& 0\\ x^{2}& x& x+3\end{matrix}|=0$, then values of $x$ are ________.
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Triangular matrix determinant = product of diagonal entries.
Updated On: Jun 26, 2026
- 2, 3
- -2, 3
- -2, -3
- 1, 2, 3
- -1, 2, -3
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The Correct Option is C
Solution and Explanation
Step 1: Concept
The determinant of a triangular matrix is the product of its diagonal elements.
Step 2: Meaning
The matrix is lower triangular (all elements above main diagonal are 0).
Step 3: Analysis
$Det = 1 \times (x+2) \times (x+3) = 0$.
Step 4: Conclusion
$x+2 = 0 \implies x = -2$; $x+3 = 0 \implies x = -3$. Final Answer: (C)
The determinant of a triangular matrix is the product of its diagonal elements.
Step 2: Meaning
The matrix is lower triangular (all elements above main diagonal are 0).
Step 3: Analysis
$Det = 1 \times (x+2) \times (x+3) = 0$.
Step 4: Conclusion
$x+2 = 0 \implies x = -2$; $x+3 = 0 \implies x = -3$. Final Answer: (C)
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