No menu items!

Determinant of a 1 x 1 Matrix

-

A matrix is nothing but a collection of numbers arranged in rectangular boxes. Hence a 1 x 1 matrix having only one row and one column is nothing but the scalar/number itself and the determinant is equal to the value of the scalar.

Example of a 1 x 1 matrix with positive determinant:

Consider the matrix shown below.

Example of a 1 x 1 Matrix

The above matrix has determinant equal to 7. Since the determinant is nonzero the equation Ax = 0 must have only the trivial solution. This is clearly true since the equation 7x = 0 \text{ has } x = 0 as the only solution. This also gives us some motivation for why the determinant of a 1 x 1 matrix is defined in the manner above.

Example of a 1 x 1 matrix with determinant zero:

The matrix shown below clearly has determinant equal to zero.

Example of a 1 x 1 singular Matrix

This means that the equation Ax = 0 must have a non-trivial solution. This is clearly true since the equation 0x = 0 is true for any value of x belonging to real numbers.

Hey ­čĹő

I'm currently pursuing a Ph.D. in Maths. Prior to this, I completed my master's in Maths & bachelors in Statistics.

I created this website for explaining maths and statistics concepts in the simplest possible manner.

If you've found value from reading my content, feel free to support me in even the smallest way you can.



Share this article

Recent posts

Popular categories

Recent comments