Systems of Equations

Below is a system of equations:

$\displaystyle x + 2y + 3z = 3$
$\displaystyle 2x - y + 4z = 5$
$\displaystyle x - 3y + 2\lambda z = 2$

Use Gaussian elimination to find the value of $\displaystyle \lambda$ which leads to redundancy.

A system of equations is defined by
$\displaystyle x - 3y + z = -1$
$\displaystyle 3x - 2y + 4z = 11$
$\displaystyle x + 4y + 2z = 15$
Use Gaussian elimination to determine whether the system shows redundancy, inconsistency or has a unique solution.

(a)Use Gaussian elimination to express $\displaystyle z$ in terms of $\displaystyle \lambda$ for the system of equations:

$\displaystyle x - y - 3z = 1$
$\displaystyle 2x - 3y - 5z = 8$
$\displaystyle x + 2y + \lambda z = -7$

(b)State the value of $\displaystyle \lambda$ for which this system is inconsistent.

(c)Determine the solution of this system when $\displaystyle \lambda = -1.$

A system of equations is given by

$\displaystyle x+y-z=9$
$\displaystyle 2x-y+3z=-2$
$\displaystyle 3x+2y-2z=21$

Use Gaussian elimination to solve this system of equations.