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---
\n" ); document.write( "-x+3y=6
\n" ); document.write( "3x-9y=9
\n" ); document.write( "---
\n" ); document.write( "copy and paste the above standard form linear equations in to this (matrix method) solver:
\n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php
\n" ); document.write( "---
\n" ); document.write( "answer:
\n" ); document.write( "This linear system is singular. It has no solution
\n" ); document.write( "---
\n" ); document.write( "check by elimination method:
\n" ); document.write( "---
\n" ); document.write( "-x + 3y = 6
\n" ); document.write( "3x - 9y = 9
\n" ); document.write( "---
\n" ); document.write( "-3x + 9y = 18
\n" ); document.write( "3x - 9y = 9
\n" ); document.write( "---
\n" ); document.write( "add the system:
\n" ); document.write( "0 = 27
\n" ); document.write( "answer:
\n" ); document.write( "This linear system is singular. It has no solution.
\n" ); document.write( "NOTE: elimination method agrees with matrix method
\n" ); document.write( "---
\n" ); document.write( "NOTE TO STUDENT:
\n" ); document.write( "solving the system manually with matrices:
\n" ); document.write( "---
\n" ); document.write( "A * X = B
\n" ); document.write( "---
\n" ); document.write( "where A:
\n" ); document.write( "[a b] = [-1 +3]
\n" ); document.write( "[c d] = [+3 -9]
\n" ); document.write( "where X:
\n" ); document.write( "[x]
\n" ); document.write( "[y]
\n" ); document.write( "where B:
\n" ); document.write( "[6]
\n" ); document.write( "[9]
\n" ); document.write( "---
\n" ); document.write( "[-1 +3][x] = [6]
\n" ); document.write( "[+3 -9][y] = [9]
\n" ); document.write( "---
\n" ); document.write( "solve for X:
\n" ); document.write( "X = (A-inverse) * B
\n" ); document.write( "---
\n" ); document.write( "where A-inverse:
\n" ); document.write( "[-9 -3] * 1/dA
\n" ); document.write( "[-3 -1]
\n" ); document.write( "---
\n" ); document.write( "NOTE:
\n" ); document.write( "let dA stand for \"the determinant of matrix A\"
\n" ); document.write( "the determinant of A is a scalar (a real number) derived from matrix A ...
\n" ); document.write( "---
\n" ); document.write( "dA = ad - bc
\n" ); document.write( "dA = (-1*-9) - (3*3)
\n" ); document.write( "dA = 9 - 9
\n" ); document.write( "dA = 0
\n" ); document.write( "---
\n" ); document.write( "1/dA = 1/0
\n" ); document.write( "but division by zero is undefined
\n" ); document.write( "---
\n" ); document.write( "recall that A-inverse is:
\n" ); document.write( "[-9 -3] * 1/dA
\n" ); document.write( "[-3 -1]
\n" ); document.write( "---
\n" ); document.write( "so A-inverse is undefined
\n" ); document.write( "---
\n" ); document.write( "recall that:
\n" ); document.write( "X = (A-inverse) * B
\n" ); document.write( "---
\n" ); document.write( "so the solution vector X is undefined !!!
\n" ); document.write( "---
\n" ); document.write( "answer:
\n" ); document.write( "Therefore, this linear system is singular. It has no solution.
\n" ); document.write( "NOTE: matrix-method solver agrees with elimination method, and both agree with the manual solution by matrices.
\n" ); document.write( "---
\n" ); document.write( "Solve and graph linear equations:
\n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php
\n" ); document.write( "---
\n" ); document.write( "Solve quadratic equations, quadratic formula:
\n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php
\n" ); document.write( "---
\n" ); document.write( "Solve systems of linear equations up to 6-equations 6-variables:
\n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php \n" ); document.write( "