NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.1 Question 5

✅ Step-by-Step Solution

1. Part 1:
2. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
3. The cofactors in this row are \(\left[\begin{matrix}-5 & -3 & 0\end{matrix}\right]\).
4. The expansion terms are \(-15\), \(3\), \(0\).
5. Adding and simplifying gives det A = \(-12\).
6. Part 2:
7. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
8. The cofactors in this row are \(\left[\begin{matrix}7 & -5 & 1\end{matrix}\right]\).
9. The expansion terms are \(21\), \(20\), \(5\).
10. Adding and simplifying gives det A = \(46\).
11. Part 3:
12. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
13. The cofactors in this row are \(\left[\begin{matrix}9 & 6 & -3\end{matrix}\right]\).
14. The expansion terms are \(0\), \(6\), \(-6\).
15. Adding and simplifying gives det A = \(0\).
16. Part 4:
17. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
18. The cofactors in this row are \(\left[\begin{matrix}-5 & -3 & -6\end{matrix}\right]\).
19. The expansion terms are \(-10\), \(3\), \(12\).
20. Adding and simplifying gives det A = \(5\).