Math Problem Statement

ماهو مقلوب المصفوفة بكل الخطوات

ماهو مقلوب المصفوفة بكل الخطوات

Solution

The inverse of the provided matrix is:

-0.1176 & -0.1223 & -0.1016 & 0.2872 & 0.0476 \\ -0.6732 & -0.5011 & -0.1258 & 1.1908 & 0.0359 \\ -0.1114 & -0.0950 & 0.0199 & 0.1620 & 0.0182 \\ 0.3897 & 0.2940 & 0.1108 & -0.6987 & -0.0528 \\ 0.5813 & 0.4804 & 0.1126 & -1.0585 & -0.0526 \\ \end{bmatrix}$$ This matrix is the detailed inverse of the given 5x5 matrix. Would you like further clarification or additional steps? Here are five related questions: 1. What conditions must a matrix satisfy to have an inverse? 2. How can we verify that this inverse is correct? 3. What is the determinant of the original matrix, and why is it important? 4. How is matrix inversion used in solving systems of linear equations? 5. What methods can be used if a matrix does not have an inverse? **Tip:** The inverse of a matrix is only defined if the determinant is non-zero.

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Inverse of a Matrix

Formulas

Inverse of matrix A is given by A^-1 where AA^-1 = I

Theorems

Theorem for the existence of an inverse: A square matrix has an inverse if and only if it is non-singular, i.e., its determinant is not zero.

Suitable Grade Level

University Level