[[a + 2b], [3a - 4]] =( matrix 2a-b\\ 5a-2b matrix )

It seems like you're dealing with a system of matrix equations. Let's break this down.

You have a matrix equation:

\[
\begin{bmatrix} 
a + 2b \\
3a - 4 
\end{bmatrix}
=
\begin{bmatrix} 
2a - b \\
5a - 2b 
\end{bmatrix}
\]

To solve this, we'll equate the corresponding elements of the two matrices:

1. For the first row: 
\[
a + 2b = 2a - b
\]

2. For the second row:
\[
3a - 4 = 5a - 2b
\]

Now, let's solve each equation separately.

### 1. Solve for \(a + 2b = 2a - b\):
\[
a + 2b = 2a - b
\]
Subtract \(a\) from both sides:
\[
2b = a - b
\]
Add \(b\) to both sides:
\[
3b = a
\]
So,
\[
a = 3b
\]

### 2. Solve for \(3a - 4 = 5a - 2b\):
Substitute \(a = 3b\) into this equation:
\[
3(3b) - 4 = 5(3b) - 2b
\]
Simplify:
\[
9b - 4 = 15b - 2b
\]
\[
9b - 4 = 13b
\]
Subtract \(9b\) from both sides:
\[


Explore how to solve matrix equations with a detailed example and step-by-step solution. This problem involves equating elements of matrices and solving linear algebra equations. Suitable for college-level students studying linear algebra.

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