Linear Algebra Quiz

Clint Givens
Quiz by Clint Givens, updated more than 1 year ago
Clint Givens
Created by Clint Givens over 7 years ago
172
3

Description

This quiz tests your detailed understanding of concepts and results in elementary linear algebra.

Resource summary

Question 1

Question
A matrix has determinant zero if and only if it is ...
Answer
  • singular
  • invertible
  • square
  • diagonal

Question 2

Question
A matrix which represents a linear transformation \(T: \mathbb{R}^2 \to \mathbb{R}^3\) has dimensions ...
Answer
  • 2x3
  • 3x2
  • 2x3 or 3x2
  • 3x3
  • 2x2
  • 2x2 or 3x3
  • There is no matrix representation for such a transformation.

Question 3

Question
A linear system of two equations with three unknowns could have ...
Answer
  • no solutions
  • exactly one solution
  • infinitely many solutions

Question 4

Question
Which of the following are possible values for the rank of a 3x5 matrix?
Answer
  • 1
  • 3
  • 4
  • 5
  • 8
  • 15

Question 5

Question
Which of the following are elementary row operations?
Answer
  • Multiplying each entry in the row by a nonzero constant
  • Interchanging the position of two rows
  • Replacing a row with the sum of itself and a multiple of another row
  • Rearranging the order of the entries within a row
  • Replacing a row with the sum of two other rows
  • Adding a nonzero constant to each entry in a row
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