Question

Let A = \begin{pmatrix} 1 & 1 & 1 & 1 \\ 0 & 1 & 2 & -1 \\ 1 & 2 & 3 & 0 \\ 2 & 3 & 4 & 1 \end{pmatrix}. \\ 1 Find the basic solutions to the homogeneous system Ax = 0. \\ 2 Verify that x = \begin{pmatrix} -1 \\ 2 \\ 0 \\ 0 \end{pmatrix} is a solution to Ax = \begin{pmatrix} 1 \\ 2 \\ 3 \\ 4 \end{pmatrix} by computing Ax (not by working with the augmented matrix for this system). \\ 3 Find all solutions to the system Ax = \begin{pmatrix} 2 \\ 1 \\ 3 \\ 5 \end{pmatrix} using Theorem 3 from the 2.1-2.3 pre-class reading (see p.9) together with your work from 4.1 & 4.2.

          Let A = \begin{pmatrix} 1 & 1 & 1 & 1 \\ 0 & 1 & 2 & -1 \\ 1 & 2 & 3 & 0 \\ 2 & 3 & 4 & 1 \end{pmatrix}. \\ 1 Find the basic solutions to the homogeneous system Ax = 0. \\ 2 Verify that x = \begin{pmatrix} -1 \\ 2 \\ 0 \\ 0 \end{pmatrix} is a solution to Ax = \begin{pmatrix} 1 \\ 2 \\ 3 \\ 4 \end{pmatrix} by computing Ax (not by working with the augmented matrix for this system). \\ 3 Find all solutions to the system Ax = \begin{pmatrix} 2 \\ 1 \\ 3 \\ 5 \end{pmatrix} using Theorem 3 from the 2.1-2.3 pre-class reading (see p.9) together with your work from 4.1 & 4.2.

Let A =
< p m a t r i x >
.
1 Find the basic solutions to the homogeneous system Ax = 0.
2 Verify that x =
< p m a t r i x >
is a solution to Ax =
< p m a t r i x >
by computing Ax (not by working with the augmented matrix for this system).
3 Find all solutions to the system Ax =
< p m a t r i x >
using Theorem 3 from the 2.1-2.3 pre-class reading (see p.9) together with your work from 4.1 4.2.

Added by Gabriel A.

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