Question

Std 11 Determinants..
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Solve the linear equation using cramer's rule
(-2)/(x)-(1)/(y)-(3)/(z)=3
(2)/(x)-(3)/(y)+(1)/(z)=-13
(2)/(x)-(3)/(z)=-11​

Answer 1

Answer:

Step-by-step explanation:

Given:

$\frac{-2}{x}-\frac{1}{y} -\frac{3}{z} =3\\ \\ \frac{2}{x}-\frac{3}{y} +\frac{1}{z} =-13\\ \\ \frac{2}{x} -\frac{3}{z} =-11$

To find: Solve the equations using cramer's rule

Solution:

Step 1: Let

$\frac{1}{x}=a\\ \\\frac{1}{y}=b\\ \\ \frac{1}{z}=c$

Thus, equations can be written as

$-2a-b-3c=3\\ 2a-3b+c=-13\\ 2a-3c=-11$

Step 2: Create matrix AX=B

$\left[\begin{array}{ccc}-2&-1&-3\\2&-3&1\\2&0&-3\end{array}\right] \left[\begin{array}{c}a&b&c\end{array}\right] =\left[\begin{array}{c}3&-13&-11\end{array}\right]$

Step 3: Find determinant of A

$\left|\begin{array}{ccc}-2&-1&-3\\2&-3&1\\2&0&-3\end{array}\right|=-2(9)+1(-6-2)-3(6)$

Δ= -18-8-18

Δ=-44

Step 4: Find Value of a

a=Δ1/Δ

$a=\frac{\left|\begin{array}{ccc}3&-1&-3\\-13&-3&1\\-11&0&-3\end{array}\right| }{-44} \\ \\ a=\frac{176}{-44} \\ \\ a=-4$

Step 5: Find the valuue of b

b=Δ2/Δ

$b=\frac{\left|\begin{array}{ccc}-2&3&-3\\2&-13&1\\2&-11&-3\end{array}\right| }{-44} \\ \\ b=\frac{-88}{-44} \\ \\ b=2$

Step 6:Find value of c

c=Δ3/Δ

$c=\frac{\left|\begin{array}{ccc}-2&-1&3\\2&-3&-13\\2&0&-11\end{array}\right| }{-44} \\ \\ c=\frac{-44}{-44} \\ \\ c=1$

Step 7: Find the value of x,y and z

$x=\frac{-1}{4} \\ \\ y=\frac{1}{2}\\ \\ z=1$

Final answer:

Solution of linear equation using cramer's rule has been done.

$\bold{x=-\frac{1}{4}} \\ \\\bold{ y=\frac{1}{2}}\\ \\ \bold{z=1}$

Hope it helps you.

To learn more on brainly:

i. by using Cramer's rule and Matrix inversion method, when the coefficient matrix is nonsingular

ii. by using Gauss-Jordan method. Also determine whether the system has a unique solution or infinite number of solutions or no solution. Find the solution if exist.

5x - 6y + 4z = 157x + 4y - 3z = 192x + y + 6z = 46

https://brainly.in/question/7029463