BCA 1001Ultimate Handwritten Matrices & Determinants Notes | Clear, Colorful & Exam-Ready

■ 50 Practice Questions — Matrices & Determinants (Basic
to Hard)

For BCA / Class 12 / First-Year University — Compiled by Zapdo ■

1. Define a matrix and write its order for A = [[2,3,4],[1,5,6]].

2. Find x if [[2,x],[5,7]] = [[2,3],[5,7]].

3. Find A+B and A−B for A=[[2,0],[1,3]], B=[[1,4],[0,2]].

4. Find transpose of A=[[3,-2],[5,7],[1,0]].

5. Check equality of A=[[2,3],[4,5]] and B=[[2,3],[4,5]].

6. Find determinant of A=[[2,3],[5,7]].

7. Evaluate |1 2 3; 2 3 1; 3 1 2|.

8. Prove |A|=ad−bc for A=[[a,b],[c,d]].

9. Find x if |2 3 1; 1 x 4; 3 2 5|=0.

10. Find minors and cofactors of [[1,2,3],[0,4,5],[1,0,6]].

11. Find A■¹ using adjoint for A=[[2,3],[1,4]].

12. Prove |1 1 1; a b c; a² b² c²|=(b−a)(c−a)(c−b).

13. Find AB and BA for A=[[1,2],[3,4]], B=[[2,0],[1,2]].

14. Find adjoint and inverse of A=[[4,7],[2,6]].

15. Solve 2x+y=5, x−y=1 by matrix method.

16. If A=[[1,2,3],[0,1,4],[5,6,0]], find A■ and |A|.

17. Find x,y if [[2,x],[3,4]]+[[1,2],[y,0]]=[[3,4],[5,4]].

18. Verify (AB)■=B■A■ for A=[[1,2],[3,4]], B=[[2,0],[1,2]].

19. Solve [[1,2],[3,4]][[x],[y]]=[[5],[11]].

20. Give one symmetric and one skew-symmetric example.

21. Find A■¹ for [[1,2,3],[0,1,4],[5,6,0]].

22. Find k if |2 3 1; 4 k 6; 3 2 5|=0.

23. Find A²−5A+6I for A=[[2,1],[0,3]].

24. Prove |a a² 1; b b² 1; c c² 1|=(a−b)(b−c)(c−a).

25. Find inverse of [[2,−1],[1,3]] and verify AA■¹=I.

26. If |2 3; 5 x|=1, find x.

27. Evaluate |cosA sinA 1; cosB sinB 1; cosC sinC 1|.

28. Show |1 1 1; 1 2 3; 1 3 6|=1.