DeterminantSteps - Maple Help

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

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

Compatibility

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