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Question 824678: Solve using matrices
-x+3y=6
3x-9y=9
Help please!
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
-x+3y=6
3x-9y=9
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copy and paste the above standard form linear equations in to this (matrix method) solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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answer:
This linear system is singular. It has no solution
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check by elimination method:
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-x + 3y = 6
3x - 9y = 9
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-3x + 9y = 18
3x - 9y = 9
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add the system:
0 = 27
answer:
This linear system is singular. It has no solution.
NOTE: elimination method agrees with matrix method
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NOTE TO STUDENT:
solving the system manually with matrices:
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A * X = B
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where A:
[a b] = [-1 +3]
[c d] = [+3 -9]
where X:
[x]
[y]
where B:
[6]
[9]
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[-1 +3][x] = [6]
[+3 -9][y] = [9]
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solve for X:
X = (A-inverse) * B
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where A-inverse:
[-9 -3] * 1/dA
[-3 -1]
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NOTE:
let dA stand for "the determinant of matrix A"
the determinant of A is a scalar (a real number) derived from matrix A ...
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dA = ad - bc
dA = (-1*-9) - (3*3)
dA = 9 - 9
dA = 0
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1/dA = 1/0
but division by zero is undefined
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recall that A-inverse is:
[-9 -3] * 1/dA
[-3 -1]
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so A-inverse is undefined
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recall that:
X = (A-inverse) * B
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so the solution vector X is undefined !!!
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answer:
Therefore, this linear system is singular. It has no solution.
NOTE: matrix-method solver agrees with elimination method, and both agree with the manual solution by matrices.
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https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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