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I can help solve the exercises shown in the image. Let's begin by focusing on Exercise 60, which asks to solve the matrix equation \( A\mathbf{x} = \mathbf{b} \) for the vector \( \mathbf{x} \).

#### 60(a):
The system given is:
\[
A = \begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}, \quad \mathbf{b} = \begin{bmatrix} 5 \\ 6 \end{bmatrix}
\]

To solve \( A\mathbf{x} = \mathbf{b} \), we can use matrix inversion or Gaussian elimination.

Would you like a detailed solution for each method (Gaussian or inverse matrix)? After this, we can proceed to the next part.

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**Relative Questions:**
1. How do you find the inverse of a 2x2 matrix?
2. What is the Gaussian elimination process for solving systems of linear equations?
3. What is the determinant, and why is it important in solving matrix equations?
4. How can you verify the solution of a system of equations?
5. What is the difference between solving a system using Cramer's rule and Gaussian elimination?

**Tip:** When using matrix inversion to solve \( A\mathbf{x} = \mathbf{b} \), ensure that the determinant of \( A \) is non-zero, as a zero determinant means the matrix is singular and not invertible.

Solve the system of linear equations given by the matrix equation Ax = b using Cramer's rule and the Gauss-Jordan elimination method.

Learn how to solve matrix equations using Cramer's Rule and the Gauss-Jordan Elimination method. This guide covers key linear algebra concepts such as determinants, matrix inverses, and row reduction. Suitable for college-level students studying linear systems.

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