Question

Q1.Using matrices, solve the following system of equations: 3x-y+z=5 , 2x-2y+3z=7 , x+y-z=-1​

Answer 1

Step-by-step explanation:

Given :

3x-y+z=5 , 2x-2y+3z=7 , x+y-z=-1

To Find : Solve Using matrices,

Solution:

3x-y+z=5 ,

2x-2y+3z=7 ,

x+y-z=-1

$\begin{gathered}\left[\begin{array}{ccc}3&-1&1\\2&-2&3\\1&1&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}5\\7\\1\end{array}\right]\end{gathered}$

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

$\begin{gathered}X=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\end{gathered} </p><p>$

$\begin{gathered}B= \left[\begin{array}{ccc}5\\7\\1\end{array}\right]\end{gathered} </p><p>$

X = A⁻¹B

| A | = 3(2 - 3) - (-1)(-2 - 3) + 1(2 - (-2))

= -3 - 5 + 4

= - 4

A⁻¹ = Adj A / | A |

$\begin{gathered}Adj A =\left[\begin{array}{ccc}-1&0&-1\\5&-4&-7\\4&-4&-4\end{array}\right]\end{gathered}$

$\begin{gathered}X=\dfrac{-1}{4} \left[\begin{array}{ccc}-6\\-10\\-12\end{array}\right]\end{gathered} </p><p>$

x = 3/2 , y = 5/2 , z = 3

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