Consider the matrix that represents a linear system: 1 0 −4 0 : 3 2 1 −10 8 : −3 0 −3 6 −24 : 27 x y z w : b (a)  Use row reduction (Gaussian elimination) to obtain the Reduced Echelon Form of the matrix. Important: Use row operation notation to indicate steps. (b)From the reduced echelon form of the matrix of part (a) indicate: Which variables are independent (called

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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(2) Consider the matrix that represents a linear system:
1 0 −4 0 : 3
2 1 −10 8 : −3
0 −3 6 −24 : 27
x y z w : b
(a)  Use row reduction (Gaussian elimination) to obtain the Reduced Echelon Form of the matrix. Important: Use row operation notation to indicate steps.
(b)From the reduced echelon form of the matrix of part (a) indicate: Which
variables are independent (called “leading” in the textbook):
Which (if any) variables are free variables (also called parameters):
(c). Write out the solution to the system. If there are any free variables, indicate them clearly and solve for the independent variables in terms of the free variables

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