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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 toa)Diagonal Matrixb)Null Matrixc)Square Matrixd)Unit Matrix

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Solution

In solving simultaneous equations by the Gauss-Jordan method, the coefficient matrix is reduced to a Unit Matrix (d).

Here are the steps:

  1. Write down the augmented matrix of the system of equations.

  2. Use elementary row operations to transform the matrix into row-echelon form.

  3. 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.

  4. The resulting matrix is a unit matrix, where the main diagonal consists of ones and all other entries are zero.

  5. The solutions to the system of equations can then be read off from the last column of the matrix.

This problem has been solved

Similar Questions

In solving simultaneous equations by Gauss - Jordan method, the coefficient matrix is reduced to

In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads toa)Lower triangular matrixb)Diagonal matrixc)Upper triangular matrixd)Singular matrix

Gauss-jordan Method

matrix A use Gauss-Jordan eli

se Gauss-Jordan elimination to solve the following linear system.x2 + x3 − 2x4 = −8x1 + 2x2 − x3 − x4 = 22x1 + 4x2 + x3 − 3x4 = −7x1 + 3x2 − 7x3 − x4 = 16

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