1. You are given the following system of linear equations:
3x - 2y + z = 2
-x + y = 3
-2y + 6 = -1
Provide a coefficient matrix corresponding to the system of linear equations.
What is the inverse of this matrix?
What is the transpose of this matrix?
Find the determinant for this matrix.
Calculate the following for
A * B
2.Solve the following linear system using Gaussian elimination.
2y + z = 4
x+ y +z = 6
2x + y + z = 7
3. Solve the following linear system for x using Cramer's rule.
4x - y + z = -5
2x + 2y + 3z = 10
5x - 2y + 6z = 1
The solution contains detailed explanation of how to solve the linear equation system by using matrix method or Gaussian elimination.