NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.2 Question 1

✅ Step-by-Step Solution

1. Part 1: use Δ=½|det \(\left[\begin{matrix}1 & 0 & 1\\6 & 0 & 1\\4 & 3 & 1\end{matrix}\right]\)|.
2. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
3. The cofactors in this row are \(\left[\begin{matrix}-3 & -2 & 18\end{matrix}\right]\).
4. The expansion terms are \(-3\), \(0\), \(18\).
5. Adding and simplifying gives det A = \(15\).
6. The area is \(\frac{15}{2}\) square units.
7. Part 2: use Δ=½|det \(\left[\begin{matrix}2 & 7 & 1\\1 & 1 & 1\\10 & 8 & 1\end{matrix}\right]\)|.
8. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
9. The cofactors in this row are \(\left[\begin{matrix}-7 & 9 & -2\end{matrix}\right]\).
10. The expansion terms are \(-14\), \(63\), \(-2\).
11. Adding and simplifying gives det A = \(47\).
12. The area is \(\frac{47}{2}\) square units.
13. Part 3: use Δ=½|det \(\left[\begin{matrix}-2 & -3 & 1\\3 & 2 & 1\\-1 & -8 & 1\end{matrix}\right]\)|.
14. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
15. The cofactors in this row are \(\left[\begin{matrix}10 & -4 & -22\end{matrix}\right]\).
16. The expansion terms are \(-20\), \(12\), \(-22\).
17. Adding and simplifying gives det A = \(-30\).
18. The area is \(15\) square units.