Clint Givens
Quiz by , created more than 1 year ago

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

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Clint Givens
Created by Clint Givens over 10 years ago
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Linear Algebra Quiz

Question 1 of 5

1

A matrix has determinant zero if and only if it is ...

Select one of the following:

  • singular

  • invertible

  • square

  • diagonal

Explanation

Question 2 of 5

1

A matrix which represents a linear transformation \(T: \mathbb{R}^2 \to \mathbb{R}^3\) has dimensions ...

Select one of the following:

  • 2x3

  • 3x2

  • 2x3 or 3x2

  • 3x3

  • 2x2

  • 2x2 or 3x3

  • There is no matrix representation for such a transformation.

Explanation

Question 3 of 5

1

A linear system of two equations with three unknowns could have ...

Select one or more of the following:

  • no solutions

  • exactly one solution

  • infinitely many solutions

Explanation

Question 4 of 5

1

Which of the following are possible values for the rank of a 3x5 matrix?

Select one or more of the following:

  • 1

  • 3

  • 4

  • 5

  • 8

  • 15

Explanation

Question 5 of 5

1

Which of the following are elementary row operations?

Select one or more of the following:

  • 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

Explanation

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