4 **Section 4: Solving Systems of Linear Equations Using Inverse Matrices**Use your graphing calculator to its fullest capacity. Apply the inverse matrix approach to solve the system of linear equations:1. \( 3x + 2y + 2z = 7 \)2. \( 2x + y + z = -5 \)3. \( x + y + 2z = 12 \)**A. Provide the matrix equation in the form: \( AX = B \) (based on the 3 equations)**\[ X = \begin{pmatrix}x \\y \\z\end{pmatrix}\]**B. Now solve for matrix \( X \); place as a matrix equation. For example:**\[ X = \begin{pmatrix}2 & 7 & 2 \\2 & 6 & 1 \\1 & 3 & 1 \end{pmatrix}\cdot\begin{pmatrix}2 & 7 & 2 \\2 & 6 & 1 \\1 & 3 & 1 \end{pmatrix}^{-1}\]**C. What is your inverse matrix? For example: \( A^{-1} \)**\[ A^{-1} = \begin{pmatrix}7 & -1 & 0 \\-4 & 3 & 6 \\2 & 5 & -5 \end{pmatrix}\]**D. Now solve for \( x, y, \) and \( z \). Since you are using your graphing calculator for the matrix arithmetic, no work needs to be shown; the work shown above is sufficient.**\[ x = \_\_\_\_\_\_\_\_, \: y = \_\_\_\_\_\_\_\_, \: \text{and} \: z = \_\_\_\_\_\_\_\_.\]**E. Show how you would verify that your values for \( x, y, \) and \( z \) above are the solution.**In the diagrams, we have examples of matrices \( X \) and \( A^{-1} \). These matrices will be different once you calculate them based on the given linear equations. Use your graphing calculator to find the precise values and verify them by substit

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4. You may use your graphing calculator to its fullest capacity. Apply the inverse matrix approach to solve the system of linear equations: 1. 3x + 2y +2z = 7 2. 2x + y + z = -5 3. x + y + 2z = 12 X A. Provide the matrix equation in the form: AX = B (based on the 3 equations). X = y Z -1 /2 7 21 2 7 2 B. Now solve for matrix X; place as a matrix equation. For example: X = 2 6 1 2 6 3) 1 1 3 1 1 3 1 7 -1 0 C. What is your inverse matrix? For example: A-¹ = -4 3 6 2 5 -5 D. Now solve for x, y, and z. Since you are using your graphing calculator for the matrix arithmetic, no work needs to be shown; the work shown above is sufficient. X = y = and z= E. Show how would you verify your values for x, y, and z above is the solution?