Convert the augmented matrix ⎡⎣⎢⎢⎢−3−5−5−5−35−2−40⎤⎦⎥⎥⎥ [ −3 −5 −2 −5 −3 −4 −5 5 0 ] to the equivalent linear system. Use x1 and x2 to enter the variables x1 x 1 and x2 x 2 .
Question
Convert the augmented matrix ⎡⎣⎢⎢⎢−3−5−5−5−35−2−40⎤⎦⎥⎥⎥ [ −3 −5 −2 −5 −3 −4 −5 5 0 ]
to the equivalent linear system. Use x1 and x2 to enter the variables x1 x 1 and x2 x 2 .
Solution
The given augmented matrix is a representation of a system of linear equations. Each row in the matrix corresponds to an equation, and each column corresponds to a coefficient of the variables in the equations.
The given matrix is:
[-3 -5 -2] [-5 -3 -4] [-5 5 0]
This corresponds to the system of linear equations:
-3x1 - 5x2 = -2 -5x1 - 3x2 = -4 -5x1 + 5x2 = 0
So, the equivalent linear system of the given augmented matrix is:
-3x1 - 5x2 = -2 -5x1 - 3x2 = -4 -5x1 + 5x2 = 0
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