linear-equations

Let $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 3 \\ 1 & -2 & -3 \end{bmatrix}$ and $b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}$. For Ax = b to be solvable, which one of the...

For the matrix $[A] = \begin{bmatrix} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{bmatrix}$ which of the following statements is/are TRUE?

Consider the system of equations $\begin{bmatrix} 1 & 3 & 2 \\ 2 & 2 & -3 \\ 4 & 4 & -6 \\ 2 & 5 & 2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix}...

In the solution of the following set of linear equations by Gauss-elimination using partial pivoting $$$5x+y+2z=34,$$$ $$$4y-3z=12$$$ and $$$10x-2y+z=-4.$$$ The pivots for eliminat...