Math Problem Statement

Tentukan nilai a, b, dan c dari kesamaan-kesamaan matriks di bawah ini (seperti terlihat pada gambar).

Solution

Let's find the values of aa, bb, and cc from the matrix equations shown in the image. Each equation gives us a system of linear equations to solve. I will solve each part separately.

Part a

Given:

2a - 1 \\ 4b + 2 \end{pmatrix} = \begin{pmatrix} 7 - 2a \\ -10 \end{pmatrix}$$ We get two equations: 1. $$2a - 1 = 7 - 2a$$ 2. $$4b + 2 = -10$$ Let's solve these equations.For part $$a$$, we have found: - $$a = 2$$ - $$b = -3$$ ### Part b Given: \[ \begin{pmatrix} a - b \\ a + b

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Math Problem Analysis

Mathematical Concepts

Matrix Equations
Linear Algebra

Formulas

Matrix equality: For matrices to be equal, corresponding elements must be equal.
Basic linear equations: ax + b = 0

Theorems

Equality of Matrices Theorem

Suitable Grade Level

Grades 10-12

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