GRE Subject 2026 Practice Test Maths Linear Algebra Free Quiz 1

1. What is linear algebra?

A. Vectors, vector spaces, and linear transformations B. Matrices only C. Determinants only D. Equations only

2. What is the determinant of [[a,b],[c,d]]?

A. ab - cd B. ac - bd C. ad + bc D. ad - bc

3. What property does matrix multiplication have?

A. Commutative B. Associative C. Distributive D. Inverse

4. What is the inverse of a 2x2 matrix [[a,b],[c,d]]?

A. [[d,-b],[-c,a]] B. [[a,b],[c,d]] C. (1/(ad-bc))[[d,-b],[-c,a]] D. [[-d,b],[c,-a]]

5. What is a vector space?

A. A matrix B. A determinant C. A scalar D. A set with vector operations

6. What is the transpose of a matrix?

A. Inverse B. Transpose C. Determinant D. Adjugate

7. What is the rank of a matrix?

A. Dimension of column space B. Number of rows C. Number of columns D. Determinant

8. What is an eigenvector?

A. A scalar B. A vector satisfying Av = λv C. A matrix D. A determinant

9. What is the characteristic equation for eigenvalues?

A. det(A - λI) = 0 B. det(A) = 0 C. det(A - I) = 0 D. det(A + λI) = 0

10. When are two vectors orthogonal?

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