3.3 Determine solutions to a set of linear equations using the inverse matrix method. The inverse matrix method is a powerful technique for solving systems of linear equations, especially when there are multiple equations and multiple unknowns. Work with a specific system of linear equations and apply the inverse matrix method to find the solutions. Consider the following system of linear equations: 2x+3y-z=4 4x-y+2z=3 x+2y+3z=7 i. 11. 111. iv. V. vi. Create an augmented matrix from the system of linear equations. Apply the inverse matrix method to find the solutions for x, y, and z by calculating the product of the inverse of the coefficient matrix and the column vector of constants. Present the step-by-step calculation and show how to obtain the solution vector. Discuss the advantages of using the inverse matrix method for solving systems of linear equations. Explain the conditions under which the inverse matrix method is applicable, such as when the coefficient matrix is invertible. Reflect on any potential challenges or limitations of this method in practical applications.

Solve the following homogeneous system of linear equations: 3x1-6x2+9x3 = 0 -x1+2x2-3x3 = 0 3x1-6x2+9x3 = 0 If the system has no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system. You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. The system has no solution The system has no solution The system has a unique solution The system has infinitely many solutions 000 0 0 0 000

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