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Problem 357

Reduce the matrix $$ \begin{array}{rrrr} & 11 & 4 & 1 & 3 \\ & 10 & -1 & 3 & -1 \\ & A=\mid 3 & 1 & 0 & 2 \\ & 1 & -2 & 5 & 1 \end{array} \mid $$ to triangular form.

Expert verified

The matrix A in upper triangular form is:
\( A=\begin{pmatrix}
1 & -2 & 5 & 1 \\
0 & 7 & -15 & 5 \\
0 & 0 & -\frac{20}{7} & -\frac{71}{7}\\
0 & 0 & \frac{16}{7} & \frac{36}{7}
\end{pmatrix} \)

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Chapter 16

Construct a flow chart for the simplex method of linear programming.

Chapter 16

Solve the linear system $$ \begin{aligned} &14 \mathrm{x}_{1}+2 \mathrm{x}_{2}+4 \mathrm{x}_{3}=-10 \\ &16 \mathrm{x}_{1}+40 \mathrm{x}_{2}-4 \mathrm{x}_{3}=55 \\ &-2 \mathrm{x}_{1}+4 \mathrm{x}_{2}-16 \mathrm{x}_{3}=-38 \end{aligned} $$ using the Jacobi iteration method.

Chapter 16

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Chapter 16

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Chapter 16

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