In solving simultaneous equations by Gauss - Jordan method, the coefficient matrix is reduced toa)Diagonal Matrixb)Null Matrixc)Square Matrixd)Unit Matrix
Question
In solving simultaneous equations by Gauss - Jordan method, the coefficient matrix is reduced to
a) Diagonal Matrix
b) Null Matrix
c) Square Matrix
d) Unit Matrix
Solution
In solving simultaneous equations by the Gauss-Jordan method, the coefficient matrix is reduced to a Unit Matrix (d).
Here are the steps:
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Write down the augmented matrix of the system of equations.
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Use elementary row operations to transform the matrix into row-echelon form.
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Continue with the row operations until the matrix is in reduced row-echelon form. This is when the leading entry in each nonzero row is a 1, and all entries in the column above and below each leading 1 are zeros.
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The resulting matrix is a unit matrix, where the main diagonal consists of ones and all other entries are zero.
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The solutions to the system of equations can then be read off from the last column of the matrix.
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