Elementary Row/Column Operations, Invertible Matrices

Grade 12 Maths Higher — Elementary Row/Column Operations, Invertible Matrices: 25 practice questions with instant scoring and explanations.

1. Elementary row operations do NOT change:
2. Swapping two rows of a matrix multiplies the determinant by:
3. Multiplying a row by scalar k multiplies determinant by:
4. Adding a multiple of one row to another row:
5. Row echelon form (REF) has:
6. Reduced row echelon form (RREF) requires:
7. A matrix is invertible if and only if:
8. For an invertible matrix A, (A⁻¹)⁻¹ =
9. If A and B are invertible n×n matrices, then (AB)⁻¹ =
10. The inverse of an upper triangular invertible matrix is:
11. If A is orthogonal, then A⁻¹ =
12. A matrix that has a row of zeros is:
13. The process of converting matrix A to identity using elementary operations finds:
14. Two matrices related by elementary row operations are:
15. The rank of a matrix equals:
16. If rank(A) < n where A is n×n, then A is:
17. The nullity of matrix A is:
18. For an m×n matrix A: rank(A) + nullity(A) =
19. If a square matrix has two identical rows, it is:
20. The Gauss-Jordan elimination method produces:
21. A matrix A is singular if det(A) =
22. For invertible A, the system Ax = b has:
23. The condition number of matrix A measures:
24. If A = [1 2; 0 3], then A⁻¹ =
25. Review question for Elementary Row/Column Operations, Invertible Matrices