GRE Subject 2026 Practice Test Maths Linear Algebra Free Quiz 2

11. What is a basis of a vector space?

A. A determinant B. A matrix C. A scalar D. A basis

12. What size matrix represents a linear transformation from R^n to R^m?

A. m × n B. n × m C. m × m D. n × n

13. What is a diagonal matrix?

A. Identity B. Symmetric C. Skew-symmetric D. Diagonal

14. What matrix satisfies A^T = A?

A. Skew-symmetric B. Symmetric C. Orthogonal D. Diagonal

15. What matrix satisfies A^T = -A?

A. Skew-symmetric B. Symmetric C. Orthogonal D. Diagonal

16. What is the determinant of the identity matrix?

A. 0 B. -1 C. Infinity D. 1

17. What is the determinant of a triangular matrix?

A. Sum B. Product C. Trace D. Zero

18. What is the null space of a matrix?

A. Null space B. Row space C. Column space D. Rank

19. What is the row space of a matrix?

A. Null space B. Column space C. Rank D. Row space

20. What does the Gram-Schmidt process do?

A. Orthonormalizes B. Diagonalizes C. Transposes D. Inverts