# Explain the difference between a matrix and a determinant?

Explain the difference between a matrix and a determinant?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Laaibah Pitt
Step 1
Matrix is a rectangular array of numbers that is represented in a row and column format. It can be of any order.
For example:
${\left[\begin{array}{c}3\\ 5\\ 6\end{array}\right]}_{3×1}{\left[\begin{array}{cc}3& 2\\ 1& 4\\ 5& 3\end{array}\right]}_{3×2}{\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]}_{2×2}$
A determinant is a number associated with a matrix. And it can be found for only square matrices.
For example:
$|\begin{array}{cc}2& 5\\ -1& 3\end{array}|=2\left(3\right)-\left(5\right)\left(-1\right)=6+5=11$
Step 2
If a scalar multiplied to a matrix then it is multiplied to all the elements of the matrix.
$3\left[\begin{array}{cc}1& -2\\ -4& 6\\ 9& 8\end{array}\right]=\left[\begin{array}{cc}3×1& 3×-2\\ 3×-4& 3×6\\ 3×9& 3×8\end{array}\right]=\left[\begin{array}{cc}3& -6\\ -12& 18\\ 27& 24\end{array}\right]$
If a scalar is multiplied to a determinant, then it is multiplied to only one row or column.
$3|\begin{array}{cc}2& 5\\ -1& 3\end{array}|=|\begin{array}{cc}2×5& 5×3\\ -1& 3\end{array}|=|\begin{array}{cc}6& 15\\ -1& 3\end{array}|$
Jeffrey Jordon