Question

Solve system of linear equations, using matrix method.
2x+y+z=1
x-2y-z=3/2
3y-5z=9

Answer 1

Given : 2x+y+z=1

x-2y-z=3/2

3y-5z=9

To Find : Solve using matrix method.

Solution:

2x+y+z=1

x-2y-z=3/2

3y-5z=9

$\left[\begin{array}{ccc}2&1&1\\1&-2&-1\\0&3&-5\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}1\\3/2\\9\end{array}\right]$

$\left|\begin{array}{ccc}2&1&1\\1&-2&-1\\0&3&-5\end{array}\right|=34$

$Adj A =\left[\begin{matrix}13 & 8 & 1 \\5 & -10 & 3 \\3 & -6 & -5\end{matrix}\right]$

A⁺¹  = Adj A / | A |

$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\dfrac{1}{34} \left[\begin{matrix}13 & 8 & 1 \\5 & -10 & 3 \\3 & -6 & -5\end{matrix}\right] \left[\begin{array}{ccc}1\\3/2\\9\end{array}\right]$

 $\left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\1/2\\-3/2\end{array}\right]$

x = 1

y = 1/2

z = - 3/2

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