Solutions of Linear Systems II

Write a short paragraph to answer each of the following questions about solutions of systems of linear equations. You should not perform any calculations, but instead base your explanations on the appropriate properties.

[3] Consider the two systems represented by the augmented matrices.

[ 1 1 -5 3; 1 0 -2 1; 2 -1 -1 0] [ 1 1 -5 -9; 1 0 -2 -3; 2 -1 -1 0]

If the first system is known to be consistent, explain why the second system is also consistent. Do not perform any row operations.

[4] The vectors x1 and x2 are solutions of the linear system Ax=b. Is the vector 2x1-3x2 also a solution? Why or why not?