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We are asked to evaluate \( G + 2H \), where the matrices \( G \) and \( H \) are given as:

\[
G = \begin{bmatrix} 5 & 6 & 1 \\ -2 & 4 & 3 \end{bmatrix}, \quad H = \begin{bmatrix} -5 & 0 \\ 3 & 9 \\ 2 & 2 \end{bmatrix}
\]

### Step 1: Multiply matrix \( H \) by 2

To calculate \( 2H \), we multiply each element of \( H \) by 2:

\[
2H = 2 \times \begin{bmatrix} -5 & 0 \\ 3 & 9 \\ 2 & 2 \end{bmatrix} = \begin{bmatrix} -10 & 0 \\ 6 & 18 \\ 4 & 4 \end{bmatrix}
\]

### Step 2: Add \( G \) and \( 2H \)

Now, we add the two matrices \( G \) and \( 2H \):

\[
G + 2H = \begin{bmatrix} 5 & 6 & 1 \\ -2 & 4 & 3 \end{bmatrix} + \begin{bmatrix} -10 & 0 \\ 6 & 18 \\ 4 & 4 \end{bmatrix}
\]

However, the addition of two matrices is only possible if they have the same dimensions. \( G \) is a \( 2 \times 3 \) matrix, and \( H \) is a \( 3 \times 2 \) matrix, so their dimensions do not match. **Thus, the operation \( G + 2H \) is not possible** due to the dimension mismatch.

Would you like further details on matrix operations or anything else?

### Relative Questions:
1. What is the condition for two matrices to be added or subtracted?
2. How is matrix multiplication different from matrix addition?
3. Can you give an example of multiplying two matrices?
4. How are scalar multiples of a matrix computed?
5. Why do matrices need to have matching dimensions for addition?

**Tip:** Always check the dimensions of matrices before attempting to add or subtract them!

Evaluate G + 2H if possible, where G and H are given matrices.

Learn how to evaluate G + 2H for given matrices G and H. Explore matrix addition, scalar multiplication, and the conditions required for these operations. Understand why the operation is not possible in this case due to dimension mismatch.

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