The figure to the right shows the letter $\mathrm{L}$ in a rectangular coordinate system. The figure can be represented by the matrix B, shown to the right. Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The $L$ is completed by connecting the last point in the matrix, $(0,6)$, to the starting point, $(0,0)$. Use matrix operations to move the $L 3$ units to the right and 2 units up. Then graph the $L$ and its transformation in a rectangular coordinate system.
Determine the matrix operation that will move the L 3 units to the right and 2 units up and perform the operation. What is the result?

Step 1 ：The figure of the letter L is represented by the matrix B, where each column describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, \((0,6)\), to the starting point, \((0,0)\).

Step 2 ：To move the figure 3 units to the right and 2 units up, we need to add 3 to the x-coordinates and 2 to the y-coordinates. In terms of matrix operations, this means adding a matrix where each column is [3, 2] to the original matrix B.

Step 3 ：The original matrix B is \[\begin{bmatrix} 0 & 0 & 0 & 6 \\ 0 & 6 & 6 & 6 \end{bmatrix}\]

Step 4 ：The matrix to be added is \[\begin{bmatrix} 3 & 3 & 3 & 3 \\ 2 & 2 & 2 & 2 \end{bmatrix}\]

Step 5 ：Adding these two matrices together gives the new matrix B, which is \[\boxed{\begin{bmatrix} 3 & 3 & 3 & 9 \\ 2 & 8 & 8 & 8 \end{bmatrix}}\]

Step 6 ：This new matrix represents the L moved 3 units to the right and 2 units up.