DeterminantSteps - Maple Help
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Student[LinearAlgebra]

 DeterminantSteps
 show steps in finding the determinant of a square matrix

 Calling Sequence Student[LinearAlgebra][DeterminantSteps](m, opts)

Parameters

 m - square matrix to find the determinant of opts - options of the form keyword=value

Description

 • 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.

Package Usage

 • 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](..).

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{LinearAlgebra}}\right):$
 > $P≔\mathrm{Matrix}\left(\left[\left[1,3,2\right],\left[2,3,1\right],\left[2,2,1\right]\right]\right)$
 $\left[\begin{array}{rrr}1& 3& 2\\ 2& 3& 1\\ 2& 2& 1\end{array}\right]$ (1)
 > $\mathrm{DeterminantSteps}\left(P\right)$
 $\begin{array}{lll}\text{•}& {}& \text{Let's find the determinant}\\ {}& {}& \left[\begin{array}{ccc}{1}& {3}& {2}\\ {2}& {3}& {1}\\ {2}& {2}& {1}\end{array}\right]\\ \text{•}& {}& \text{Use cofactor expansion on the}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}3\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{by}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}3\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{matrix}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Find the determinant of the 2 by 2 matrices by multiplying the diagonals}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Evaluate inside the brackets}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Multiply}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Evaluate}\\ {}& {}& {-3}\end{array}$ (2)
 > $A≔⟨⟨8,4,-1,-5⟩|⟨4,2,-0.5,-2.5⟩|⟨-5,-2,3,-1⟩|⟨-5,-2.5,-4,-9⟩⟩$
 $\left[\begin{array}{cccc}8& 4& -5& -5\\ 4& 2& -2& -2.5\\ -1& -0.5& 3& -4\\ -5& -2.5& -1& -9\end{array}\right]$ (3)
 > $\mathrm{DeterminantSteps}\left(A\right)$
 $\begin{array}{lll}\text{•}& {}& \text{Let's find the determinant}\\ {}& {}& \left[\begin{array}{cccc}{8}& {4}& {-5}& {-5}\\ {4}& {2}& {-2}& {-2.5}\\ {-1}& {-0.5}& {3}& {-4}\\ {-5}& {-2.5}& {-1}& {-9}\end{array}\right]\\ \text{•}& {}& \text{Subtract}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}2\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{times column}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}2\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{from column}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}1\\ {}& {}& \left[\begin{array}{cccc}{0}& {4}& {-5}& {-5}\\ {0}& {2}& {-2}& {-2.5}\\ {0}& {-0.5}& {3}& {-4}\\ {0}& {-2.5}& {-1}& {-9}\end{array}\right]\\ \text{•}& {}& \text{Since there is a zero column}\\ {}& {}& {0}\end{array}$ (4)
 > $\mathrm{DeterminantSteps}\left(\mathrm{Matrix}\left(\left[\left[7,5\right],\left[2,3\right]\right]\right),\mathrm{output}=\mathrm{printf}\right)$
 • 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
 > $\mathrm{DeterminantSteps}\left(\mathrm{Matrix}\left(\left[\left[7,5\right],\left[2,3\right]\right]\right)\right)$
 $\begin{array}{lll}\text{•}& {}& \text{Let's find the determinant}\\ {}& {}& \left[\begin{array}{cc}{7}& {5}\\ {2}& {3}\end{array}\right]\\ \text{•}& {}& \text{Find the determinant of the 2 by 2 matrix by multiplying the diagonals}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Evaluate}\\ {}& {}& {11}\end{array}$ (5)

Compatibility

 • The Student[LinearAlgebra][DeterminantSteps] command was introduced in Maple 2022.
 • For more information on Maple 2022 changes, see Updates in Maple 2022.

 See Also