NCERT Class 12 · Ch 4 Exercise 4.4 · Q5
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 5
Find the inverse, if it exists, of \(\left[\begin{matrix}2 & -2\\4 & 3\end{matrix}\right]\).
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: \(\left[\begin{matrix}\frac{3}{14} & \frac{1}{7}\\- \frac{2}{7} & \frac{1}{7}\end{matrix}\right]\)
- For a 2×2 matrix use det A=a₁₁a₂₂−a₁₂a₂₁.
- \(6\) − \(-8\) = \(14\).
- First check whether this determinant is zero.
- The cofactor matrix is \(\left[\begin{matrix}3 & -4\\2 & 2\end{matrix}\right]\).
- Transpose the cofactor matrix: adj A=\(\left[\begin{matrix}3 & 2\\-4 & 2\end{matrix}\right]\).
- Divide by det A: A⁻¹=\(\left[\begin{matrix}\frac{3}{14} & \frac{1}{7}\\- \frac{2}{7} & \frac{1}{7}\end{matrix}\right]\).
- Multiplication verifies AA⁻¹=A⁻¹A=I.
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