The DeterminantSteps command is used to show the steps of finding the determinant of a square matrix.

The DeterminantSteps supports square matrices up to 5 by 5 in size.

The displaystyle and output options can be used to change the output format.  See OutputStepsRecord for details.

This function is part of the Student[LinearAlgebra] package, so it can be used in the short form DeterminantSteps(..) only after executing the command with(Student[LinearAlgebra]). However, it can always be accessed through the long form of the command by using Student[LinearAlgebra][DeterminantSteps](..).

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$P≔\mathrm{Matrix}\left(\left[\left[1\,3\,2\right]\,\left[2\,3\,1\right]\,\left[2\,2\,1\right]\right]\right)$

$P≔\left[\begin{array}{ccc}1& 3& 2\\ 2& 3& 1\\ 2& 2& 1\end{array}\right]$

$\mathrm{DeterminantSteps}\left(P\right)$

$\begin{array}{lll}\text{•}& & \text{Let's find the determinant}\\ & & \left[\begin{array}{ccc}1& 3& 2\\ 2& 3& 1\\ 2& 2& 1\end{array}\right]\\ \text{•}& & \text{Use cofactor expansion on the}3\text{by}3\text{matrix}\\ & & 1\cdot \left[\begin{array}{cc}3& 1\\ 2& 1\end{array}\right]+\left(\mathrm{-1}\right)\cdot 3\cdot \left[\begin{array}{cc}2& 1\\ 2& 1\end{array}\right]+1\cdot 2\cdot \left[\begin{array}{cc}2& 3\\ 2& 2\end{array}\right]\\ \text{•}& & \text{Find the determinant of the 2 by 2 matrices by multiplying the diagonals}\\ & & 1\cdot \left(3\cdot 1-2\cdot 1\right)+\left(\mathrm{-1}\right)\cdot 3\cdot \left(2\cdot 1-2\cdot 1\right)+1\cdot 2\cdot \left(2\cdot 2-2\cdot 3\right)\\ \text{•}& & \text{Evaluate inside the brackets}\\ & & 1\cdot 1+\left(\mathrm{-1}\right)\cdot 3\cdot 0+1\cdot 2\cdot \left(\mathrm{-2}\right)\\ \text{•}& & \text{Multiply}\\ & & 1+0-4\\ \text{•}& & \text{Evaluate}\\ & & \mathrm{-3}\end{array}$

$A≔⟨⟨8\,4\,-1\,-5⟩\left|⟨4\,2\,-0.5\,-2.5⟩\right|⟨-5\,-2\,3\,-1⟩|⟨-5\,-2.5\,-4\,-9⟩⟩$

$A≔\left[\begin{array}{cccc}8& 4& \mathrm{-5}& \mathrm{-5}\\ 4& 2& \mathrm{-2}& \mathrm{-2.5}\\ \mathrm{-1}& \mathrm{-0.5}& 3& \mathrm{-4}\\ \mathrm{-5}& \mathrm{-2.5}& \mathrm{-1}& \mathrm{-9}\end{array}\right]$

$\mathrm{DeterminantSteps}\left(A\right)$

$\begin{array}{lll}\text{•}& & \text{Let's find the determinant}\\ & & \left[\begin{array}{cccc}8& 4& \mathrm{-5}& \mathrm{-5}\\ 4& 2& \mathrm{-2}& \mathrm{-2.5}\\ \mathrm{-1}& \mathrm{-0.5}& 3& \mathrm{-4}\\ \mathrm{-5}& \mathrm{-2.5}& \mathrm{-1}& \mathrm{-9}\end{array}\right]\\ \text{•}& & \text{Subtract}2\text{times column}2\text{from column}1\\ & & \left[\begin{array}{cccc}0& 4& \mathrm{-5}& \mathrm{-5}\\ 0& 2& \mathrm{-2}& \mathrm{-2.5}\\ 0& \mathrm{-0.5}& 3& \mathrm{-4}\\ 0& \mathrm{-2.5}& \mathrm{-1}& \mathrm{-9}\end{array}\right]\\ \text{•}& & \text{Since there is a zero column}\\ & & 0\end{array}$

$\mathrm{DeterminantSteps}\left(\mathrm{Matrix}\left(\left[\left[7\,5\right]\,\left[2\,3\right]\right]\right)\,\mathrm{output}=\mathrm{printf}\right)$

• Let's find the determinant
        Matrix(2, 2, [[7,5],[2,3]])
• Find the determinant of the 2 by 2 matrix by multiplying the diagonals
        -2*5+3*7
• Evaluate
        11

$\mathrm{DeterminantSteps}\left(\mathrm{Matrix}\left(\left[\left[7\,5\right]\,\left[2\,3\right]\right]\right)\right)$

$\begin{array}{lll}\text{•}& & \text{Let's find the determinant}\\ & & \left[\begin{array}{cc}7& 5\\ 2& 3\end{array}\right]\\ \text{•}& & \text{Find the determinant of the 2 by 2 matrix by multiplying the diagonals}\\ & & 7\cdot 3-2\cdot 5\\ \text{•}& & \text{Evaluate}\\ & & 11\end{array}$

The Student[LinearAlgebra][DeterminantSteps] command was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.