Solving Matrix Equations: Example and Step-by-Step Solution

Math Problem Statement

[[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:

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: \[

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Matrix Equations
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College Level

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