Question

Solve by matrix inverse method :
x – y + z = 1, 2x – y = 1, 3x + 3y – 4z = 2.

Answer 1

Given :

x – y + z = 1,  2x – y = 1, 3x + 3y – 4z = 2.

To Find : Solve by matrix inverse method :

Solution:

x – y + z = 1,

2x – y  + 0.z = 1

3x + 3y – 4z = 2

AX = B

$A=\left[\begin{array}{ccc}1&-1&1\\2&-1&0\\3&3&-4\end{array}\right]$

$B = \left[\begin{array}{ccc}1 \\1\\2\end{array}\right]$

X  =  A⁻¹B

| A|  =   5

A⁻¹ = Adj A/ | A |

$A^{-1}=\dfrac{1}{5} \left[\begin{array}{ccc}4&-1&1\\8&-7&2\\9&-6&1\end{array}\right]$

  $X=\dfrac{1}{5} \left[\begin{array}{ccc}5\\5\\5\end{array}\right]$

$X = \left[\begin{array}{ccc}1\\1\\1\end{array}\right]$

x = 1 , y = 1 , z = 1

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