You & maths

Exercise Set 1.1 – No. 6

6. Fnd a linear system in the unknowns x1,x2,x3,…, that corresponds to the given augmented matrix.

\large {\color{Blue} (a) \begin{bmatrix} 0 & 3 & -1 & -1 & -1\\ 5 & 2 & 0 & -3 & -6 \end{bmatrix} }

Consider the matrix \large {\color{Blue} A= \begin{bmatrix} 0 & 3 & -1 & -1 & -1\\ 5 & 2 & 0 & -3 & -6 \end{bmatrix} }

We have that the linear system of two equations in the four unknowns x1, x2, x3, and x4 given by 

\large {\color{Blue} \begin{matrix} 3x_2-x_3-x_4 = -1 \\ 5x_1+2x_2-3x_4 = -6 \end{matrix} }

has A as its augmented matrix.

\large {\color{Blue} (b) \begin{bmatrix} 3 & 0 & 1 & -4 & 3\\ -4 & 0 & 4 & 1 & -3\\ -1 & 3 & 0 & -2 & -9\\ 0 & 0 & 0 & -1 & -2 \end{bmatrix} }

Consider the matrix \large {\color{Blue} A= \begin{bmatrix} 3 & 0 & 1 & -4 & 3\\ -4 & 0 & 4 & 1 & -3\\ -1 & 3 & 0 & -2 & -9\\ 0 & 0 & 0 & -1 & -2 \end{bmatrix} }

We have that the linear system of two equations in the four unknowns x1, x2, x3, and x4 given by 

\large {\color{Blue} \begin{matrix} 3x_1+x_3-4x_4 = 3 \\ -4x_1+4x_3+x_4 = -3 \\ -x_1+3x_3-2x_4 = -9 \\ -x_4 = -2 \end{matrix} }

has A as its augmented matrix.