# Math Help - How i solve this 2 queation in matrix .

1. ## How i solve this 2 queation in matrix .

How i solve this 2 queation in matrix .

1 - Solve the folloeing equation for I1 , I2 , I3 using Matrix Inverse method
I1 - I2 + I3 = 0
I1 + I2 = 10
I2 + 2I3 = 10

Is this first step are correct :

(1 - 1 1) (I1) = (0 )
(1 1 0) (I2) = (10 )
(0 1 2 ) (I3) = (10)

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Q2 : Check for conisitency
a ) 2X + 3y = 5 , 4X + 6y = 7
B ) 4X - 3y = 8 , 2X + 4y = 6
C )3x + 5Z = 9 , 3X - Z = 5

How i can solve like this 2 quetions

2. Hello, r-soy!

1) Solve this system using Matrix Inverse method.
. . $\begin{array}{ccc}x - y + z &=& 0 \\
x + y &=& 10 \\ y + 2z &=& 10 \end{array}$

Is this first step correct? . Yes!

. . $\begin{pmatrix}1&\text{-}1&1 \\ 1&1&0 \\ 0&1&2\end{pmatrix} \begin{pmatrix}x\\y\\z\end{pmatrix} \;=\;\begin{pmatrix}0 \\ 10 \\ 10 \end{pmatrix}$

(2) Check for consistency.

. . $(a)\;\begin{array}{ccc}2x + 3y &=& 5 \\ 4x + 6y &=& 7 \end{array} \qquad (b)\;\begin{array}{ccc}4x-3y&=& 8 \\ 2x+4y&=&6 \end{array} \qquad (c)\;\begin{array}{ccc}3x+5z &=& 9 \\ 3x-z &=& 5 \end{array}$

Evaluate the determinant of the coefficients.
If the determinant is zero, the system is inconsistent.

$(a)\;\left|\begin{array}{cc} 2&3\\4&6\end{array}\right| \:=\:12-12 \:=\:0\qquad\text{Inconsistent}$

$(b)\;\left|\begin{array}{cc}4&\text{-}3 \\ 2&4\end{array}\right| \:=\:16-(\text{-}6) \:\neq \:0\qquad\text{Consistent}$

$(c)\;\left|\begin{array}{cc}3 & 5 \\ 3 & \text{-}1\end{array}\right| \;=\;-3 -15 \:\neq\:0\qquad\text{Consistent}$

3. THANKS