Math Problem Statement

Solve in matrix form

Solution

The image shows a problem related to matrix algebra. From the image, we can extract the following information:

  • You have a system of linear equations given in matrix form as AX=BAX = B.
  • The matrix AA is a 3×33 \times 3 matrix, which is given as:
1 & 1 & -2 \\ 1 & -1 & 3 \\ 2 & -2 & 1 \end{pmatrix}$$ - The matrix $$B$$ is a $$3 \times 1$$ column matrix, given as: $$B = \begin{pmatrix} -5 \\ 4 \\ 9 \end{pmatrix}$$ The problem requires finding the matrix $$X$$, which satisfies the equation $$AX = B$$. ### Solution Steps: 1. **Matrix Form of the Equation**: The equation is $$AX = B$$, where $$A$$ is a $$3 \times 3$$ matrix, $$X$$ is a $$3 \times 1$$ column matrix (which we need to find), and $$B$$ is a $$3 \times 1$$ column matrix. 2. **Inverse of Matrix $$A$$**: To find $$X$$, you need to multiply both sides of the equation by the inverse of $$A$$: $$X = A^{-1}B$$ First, we need to calculate the inverse $$A^{-1}$$ of matrix $$A$$. 3. **Calculate the Inverse $$A^{-1}$$**: The inverse of a $$3 \times 3$$ matrix $$A$$ can be calculated using the formula: \[ A^{-1} = \frac{1}{\

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Systems of Linear Equations
Matrix Inverse

Formulas

Matrix equation AX = B
Inverse of a 3x3 matrix

Theorems

-

Suitable Grade Level

Advanced High School or College

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