Question

USE CRAMERS RULE TO X - X2 +4x3 = -4 - 8x, +3x2 + x3 = 8,2X1- X2 + X3 = 0.

Answer 1

Answer: Cramer’s Rule is a method for solving systems of linear equations using determinants. The given system of equations can be written in matrix form as:

​1−82​−13−1​411​​​x1​x2​x3​​​=​−480​​

Let A be the coefficient matrix and let D be its determinant. Then, according to Cramer’s Rule, the solution to the system is given by:

x1​=det(A)det(A1​)​,x2​=det(A)det(A2​)​,x3​=det(A)det(A3​)​

where A1​, A2​, and A3​ are the matrices obtained by replacing the first, second, and third columns of A with the right-hand side vector, respectively.

First, we calculate the determinant of A:

det(A)=​1−82​−13−1​411​​=1​3−1​11​​−(−1)​−82​11​​+4​−82​3−1​​=(3+1)+(8+2)+4(−8+6)=4+10−8=6

Next, we calculate the determinants of A1​, A2​, and A3​:

det(A1​)=​−480​−13−1​411​​=(−4)​3−1​11​​−(−1)​80​11​​+4​80​3−1​​=(−4)(3+1)+(8)+4(−8)=−16+8−32=−40

det(A2​)=​1−82​−480​411​​=(1)​80​11​​−(−4)​−82​11​​+(4)​−82​80​​=(8)+(32)+(64)=104

det(A3​)=​<IPAddress>−4<IPAddress><IPAddress>​​=(0)(3+<IPAddress>)−(<IPAddress>)+(<IPAddress>)=<IPAddress>

So, the solution to the system is given by:

x<​IPAddress>=<IPAddress>=<IPAddress>,x<​IPAddress>=<IPAddress>=<IPAddress>,x<​IPAddress>=<IPAddress>=<IPAddress>

Therefore, the solution to the system of equations is (x<​IPAddress>,x<​IPAddress>,x<​IPAddress>)=(<IPAddress>,<IPAddress>,<IPAddress>).

Explanation: