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hen 4-¹ = Given b == = 1 3 = 6. solve Az = A = 3 3 -1 -9 -8 3

hen 4-¹ = Given b == = 1 3 = 6. solve Az = A = 3 3 -1 -9 -8 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Matrix Inversion and Solution of Linear Systems #### Problem Statement If \[ A = \begin{bmatrix} 3 & -9 & 5 \\ 3 & -8 & 5 \\ -1 & 3 & -2 \end{bmatrix}, \] then we need to find the inverse of matrix \(A\), denoted as \( A^{-1} \): \[ A^{-1} = \begin{bmatrix} \quad \quad \quad \\ \quad \quad \quad \\ \quad \quad \quad \end{bmatrix}. \] #### Linear System Solution Given vector \(\vec{b}\): \[ \vec{b} = \begin{bmatrix} 1 \\ 3 \\ -3 \end{bmatrix}, \] we are to solve the equation \( A \vec{x} = \vec{b} \). #### Solution The solution vector \(\vec{x}\) is given by: \[ \vec{x} = \begin{bmatrix} \quad \\ \quad \\ \quad \end{bmatrix}. \] The task requires calculating \( A^{-1} \) and using it to find \(\vec{x} = A^{-1}\vec{b}\).
Transcribed Image Text:### Matrix Inversion and Solution of Linear Systems #### Problem Statement If \[ A = \begin{bmatrix} 3 & -9 & 5 \\ 3 & -8 & 5 \\ -1 & 3 & -2 \end{bmatrix}, \] then we need to find the inverse of matrix \(A\), denoted as \( A^{-1} \): \[ A^{-1} = \begin{bmatrix} \quad \quad \quad \\ \quad \quad \quad \\ \quad \quad \quad \end{bmatrix}. \] #### Linear System Solution Given vector \(\vec{b}\): \[ \vec{b} = \begin{bmatrix} 1 \\ 3 \\ -3 \end{bmatrix}, \] we are to solve the equation \( A \vec{x} = \vec{b} \). #### Solution The solution vector \(\vec{x}\) is given by: \[ \vec{x} = \begin{bmatrix} \quad \\ \quad \\ \quad \end{bmatrix}. \] The task requires calculating \( A^{-1} \) and using it to find \(\vec{x} = A^{-1}\vec{b}\).
Expert Solution
Step 1: Method

To find the inverse of  matrix we can use method of open square brackets A colon I close square brackets equals open square brackets I colon A to the power of negative 1 end exponent close square brackets

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