Certainly! Here is the transcription of the content with explanations for educational purposes:---**Problem 2: Solving a Matrix Equation**Consider the matrix equation \( Ax = b \) where:\[A = \begin{bmatrix}1 & 1 & 1 & -1 \\1 & 1 & -1 & 1 \\1 & -1 & 1 & 1 \\-1 & 1 & 1 & 1\end{bmatrix}, \quadx = \begin{bmatrix}x_1 \\x_2 \\x_3 \\x_4\end{bmatrix}, \quadb = \begin{bmatrix}0 \\0 \\0 \\5\end{bmatrix}\]**Tasks:**a) Compute the determinant of matrix \( A \), denoted as \( \text{det} A \).b) Use Cramer's rule to compute the value of \( x_3 \).---**Explanation of Tasks**- **Computing the Determinant**: - The determinant of a matrix provides important properties about the matrix, such as whether it's invertible. For a 4x4 matrix like the one given, computation involves a detailed expansion, which can be done using cofactor expansion along a row or column.- **Cramer's Rule**: - Cramer's rule is a method used to solve systems of linear equations with as many equations as unknowns, provided the determinant of the coefficient matrix is non-zero. For finding a particular variable \( x_3 \), you will replace the third column of \( A \) with the vector \( b \) and compute the determinant of this new matrix. The value of \( x_3 \) is then given by the ratio of this determinant to \( \text{det} A \).This exercise allows students to practice calculating determinants and applying Cramer's rule to a system of equations, reinforcing concepts in linear algebra.

The given problem is to find the determinant of the given matrix A and also to find the value of x3 for the linear equations Ax=b using the cramers rule.We can find the determinant of the matrix A by using column operations and then we can find the value of x3 using cramers rule formula.Solutions,a) Det(A) = -16b) Value of x3 = 5/4 = 1.25