https://file.aiquickdraw.com/mathbot/file/1726951307382ihgwlta5.jpg

Let's break down and solve the matrix expression step by step.

The given expression is:

\[
5 \begin{bmatrix} 1 & 2 \\ 3 & -4 \end{bmatrix} - 2 \begin{bmatrix} 5 & 0 \\ -6 & 7 \end{bmatrix} + 5 \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}
\]

### Step 1: Multiply the scalar by each matrix

#### First matrix:
\[
5 \begin{bmatrix} 1 & 2 \\ 3 & -4 \end{bmatrix} = \begin{bmatrix} 5(1) & 5(2) \\ 5(3) & 5(-4) \end{bmatrix} = \begin{bmatrix} 5 & 10 \\ 15 & -20 \end{bmatrix}
\]

#### Second matrix:
\[
-2 \begin{bmatrix} 5 & 0 \\ -6 & 7 \end{bmatrix} = \begin{bmatrix} -2(5) & -2(0) \\ -2(-6) & -2(7) \end{bmatrix} = \begin{bmatrix} -10 & 0 \\ 12 & -14 \end{bmatrix}
\]

#### Third matrix:
\[
5 \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} 5(1) & 5(0) \\ 5(0) & 5(1) \end{bmatrix} = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}
\]

### Step 2: Add/Subtract the matrices

Now we need to combine the results from Step 1:

\[
\begin{bmatrix} 5 & 10 \\ 15 & -20 \end{bmatrix} + \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix} - \begin{bmatrix} -10 & 0 \\ 12 & -14 \end{bmatrix}
\]

First, subtract the second matrix:
\[
\begin{bmatrix} 5 & 10 \\ 15 & -20 \end{bmatrix} - \begin{bmatrix} -10 & 0 \\ 12 & -14 \end{bmatrix} = \begin{bmatrix} 5 - (-10) & 10 - 0 \\ 15 - 12 & -20 - (-14) \end{bmatrix} = \begin{bmatrix} 15 & 10 \\ 3 & -6 \end{bmatrix}
\]

Then add the third matrix:
\[
\begin{bmatrix} 15 & 10 \\ 3 & -6 \end{bmatrix} + \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix} = \begin{bmatrix} 15 + 5 & 10 + 0 \\ 3 + 0 & -6 + 5 \end{bmatrix} = \begin{bmatrix} 20 & 10 \\ 3 & -1 \end{bmatrix}
\]

### Final Answer:
The result of the matrix operation is:

\[
\begin{bmatrix} 20 & 10 \\ 3 & -1 \end{bmatrix}
\]

Let me know if you'd like more details on the steps or have further questions!

### Related questions:
1. How do you perform scalar multiplication with matrices?
2. What is the process for matrix addition and subtraction?
3. Can matrix multiplication be performed on two non-square matrices?
4. What are some common properties of matrix operations?
5. How do identity matrices affect matrix operations?

### Tip:
Always check matrix dimensions before performing any operations to ensure they're compatible for addition, subtraction, or multiplication.

Calculate: 5 * [ [1, 2], [3, -4] ] - 2 * [ [5, 0], [-6, 7] ] + 5 * [ [1, 0], [0, 1] ]

This problem demonstrates how to perform scalar multiplication and matrix addition with step-by-step calculations. The final result is calculated by applying scalar operations to each element of a 2x2 matrix. Suitable for students in Grades 9-12.

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