Q 276 - Intermediate Algebra

Question

Explain the difference between a square matrix
and its determinant. Give an example of each.

Step-by-Step Solution

Answer

Square matrix is the matrix with same number of rows and columns.

Example: $\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$

Determinant of the matrix: Each square matrix has a real number associated with it is called its determinant.

Example: $\left|\begin{array}{cc}2& 1\\ 1& 2\end{array}\right|=3$

Step 1. To find

To write the difference between square matrix and determinant.

To give example for each.

Step 2. Difference between square matrix and determinant

Square matrix:

If a matrix has same number of rows and columns, then the matrix is called square matrix.

Determinant:

Each square matrix has a real number associated with it is called its determinant.

Step 3. Example of square matrix

Square matrix same number of rows and columns.

Let us say the rows and columns of the square matrix be $2$

So, example of square matrix is $\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$

Step 4. Example for determinant

To find the determinant of the square matrix $\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$.

$\left|\begin{array}{cc}2& 1\\ 1& 2\end{array}\right|=2\left(2\right)-1\left(1\right)$

         $=4-1$

        $=3$

The determinant of the square matrix is $3$