Intermediate Linear Algebra Concepts Test

Probe essential linear algebra topics like spans, kernels, and matrix properties through targeted questions.

#vectors#linear algebra#linear independence#rank nullity#vector spaces#eigenvalues#determinants#matrices

Total Questions

8

Difficulty Level

medium

Progress

0/0

0%

Quiz Questions

Answer all questions below and test your knowledge.

1
Compute the determinant of the 2x2 matrix [[3,1],[4,2]].
Question 1
2
A square matrix A is invertible if and only if det(A) is
Question 2
3
The characteristic equation for eigenvalues of A is
Question 3
4
By the rank-nullity theorem, for T: V → W, dim(V) equals
Question 4
5
Vectors u and v are orthogonal when their dot product u · v equals
Question 5
6
The trace of a square matrix is the sum of its
Question 6
7
A set {v1, v2, ..., vk} is linearly independent if the only solution to c1 v1 + ... + ck vk = 0 is
Question 7
8
Elementary row operations preserve the
Question 8