# Linear Algebra Quiz

Quiz by Clint Givens, updated more than 1 year ago
 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 ...
• singular
• invertible
• square
• diagonal

### Question 2

Question
A matrix which represents a linear transformation $$T: \mathbb{R}^2 \to \mathbb{R}^3$$ has dimensions ...
• 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 ...
• 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?
• 1
• 3
• 4
• 5
• 8
• 15

### Question 5

Question
Which of the following are elementary row operations?
• 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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