Question

solve 5X-Y+4Z=5,2x+3y+5z=2,7x-2y+6z=5 by cramer's rule differentiate tha following with respect x​

Answer 1

X=44

Y=55

.............. Hope it's helps you

Answer 2

Step-by-step explanation:

Given:

$5x-y+4z=5\\ 2x+3y+5z=2\\ 7x-2y+6z=5$

To find: Solve the equations using cramer's rule

Solution:

Step 1: Create matrix AX=B

$\left[\begin{array}{ccc}5&-1&4\\2&3&5\\7&-2&6\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}5\\2\\5\end{array}\right]$

Step 2: Find determinant of A

$|A|=\left|\begin{array}{ccc}5&-1&4\\2&3&5\\7&-2&6\end{array}\right|$

Δ=5(18+10)+1(12-35)+4(-4-21)

Δ=17

Step 3: Find Value of x

x=Δ1/Δ

$x=\frac{\left|\begin{array}{ccc}5&-1&4\\2&3&5\\5&-2&6\end{array}\right|}{17}\\ \\ x=\frac{51}{17}\\ \\ x=3$

Step 4: Find the valuue of y

y=Δ2/Δ

$y=\frac{\left|\begin{array}{ccc}5&5&4\\2&2&5\\7&5&6\end{array}\right|}{17}\\ \\ y=\frac{34}{17}\\ \\ y=2$

Step 5:Find value of z

z=Δ3/Δ

$z=\frac{\left|\begin{array}{ccc}5&-1&5\\2&3&2\\7&-2&5\end{array}\right|}{17}\\ \\ z=\frac{-34}{17}\\ \\ z=-2$

Differentiation of equation 1,2 and 3 with respect to x:

d(5x-y+4z)/dx=5

d(2x+3y+5z)/dx=2

d(7x-2y+6z)/dx=7

Rest all the terms will become zero as all the other terms treated as constant with respect to x.

Final answer:

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

$x=3\\ y=2\\ z=-2$

Hope it helps you.

To learn more on brainly:

1) 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

brainly.in/question/7029463

2) 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

https://brainly.in/question/19841238