Problem 1: Matrix Equation
Given:

We need to find the matrix
that satisfies the equation.
Let
be the matrix:

Performing the matrix multiplication:

Comparing this with the given matrix:

We can see that the matrices are not equal. Therefore, there is no matrix
that satisfies the given equation.
Problem 2: System of Equations
Given the system of equations:

We can solve this system using the Gauss-Jordan method.
Writing the augmented matrix:

Applying row operations to solve for the reduced row-echelon form:
Step 1: Replace Row2 with Row2 + 2 * Row1 and Row3 with Row3 + 3 * Row1

Step 2: Replace Row1 with (-1/3) * Row1

Step 3: Replace Row2 with Row2 - Row1

Step 4: Replace Row2 with (-3/11) * Row2

Step 5: Replace Row1 with Row1 + (2/3) * Row2

This matrix represents the system of equations in the reduced row-echelon form.
The solution is:
