NCERT Class 12 · Ch 4 Exercise 4.1 · Q3
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.1 Question 3
For A=\(\left[\begin{matrix}1 & 2\\4 & 2\end{matrix}\right]\), show det(2A)=4 det A.
💡 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: \(-24\) = 4 × \(-6\)
- For a 2×2 matrix use det A=a₁₁a₂₂−a₁₂a₂₁.
- \(2\) − \(8\) = \(-6\).
- Multiplying every entry by 2 multiplies each of the 2 rows by this factor.
- By multilinearity, det(cA)=cⁿdet A for an n×n matrix. Direct evaluation of the scaled matrix gives \(-24\).
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