You uploaded a set of matrix-related problems. I can solve them step by step for you. Let's start with problem 6 from the image, which involves finding the matrix $X$ that will solve the given matrix equations.

Problem 6(a):

Solve for $X$ in: $5X - \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix} = 3X - \begin{bmatrix} 5 & 2 \\ 6 & 1 \end{bmatrix}$

We can rearrange the equation as: $5X - 3X = \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix} - \begin{bmatrix} 5 & 2 \\ 6 & 1 \end{bmatrix}$ $2X = \begin{bmatrix} 1 - 5 & 0 - 2 \\ 2 - 6 & 3 - 1 \end{bmatrix}$ $2X = \begin{bmatrix} -4 & -2 \\ -4 & 2 \end{bmatrix}$

Dividing both sides by 2: $X = \begin{bmatrix} -2 & -1 \\ -2 & 1 \end{bmatrix}$

Problem 6(b):

Solve for $X$ in: $\begin{bmatrix} 2 & 1 \\ 2 & 2 \end{bmatrix} X = I_2$

This is a matrix equation where $I_2$ is the identity matrix. We need to find the inverse of the matrix on the left-hand side, as multiplying by the inverse will give $X$.

Let me calculate the inverse of the matrix and solve for $X$.The inverse of the matrix $\begin{bmatrix} 2 & 1 \\ 2 & 2 \end{bmatrix}$ is: $X = \begin{bmatrix} 1 & -0.5 \\ -1 & 1 \end{bmatrix}$

Problem 6(c):

Solve for $X$ in: $\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} X - X \begin{bmatrix} 1 & 4 \\ 2 & 0 \end{bmatrix} = \begin{bmatrix} 2 & -2 \\ 5 & 4 \end{bmatrix}$

This equation can be solved by combining like terms and solving for $X$. Let me handle that next.

Would you like me to proceed with solving part 6(c) or jump to another part?