Math Problem Statement

Tentukan nilai x pada persamaan berikut ini: 1. \( \begin{pmatrix} 2x & x \\ x & -3 \end{pmatrix} - \begin{pmatrix} -3 & 4 \\ -2 & 1 \end{pmatrix} = 0 \) 2. \( \begin{pmatrix} x+1 & 4 \\ 2x & x \end{pmatrix} = \begin{pmatrix} 6 & -6 \\ 5 & x \end{pmatrix} \) 3. \( \begin{pmatrix} 3x & 2 \\ x & 1 \end{pmatrix} = -7x - 4 \)

Solution

The image contains three matrix equations. Let's go through each one and solve for xx.


Problem 1

(2xxx3)(3421)=0\begin{pmatrix} 2x & x \\ x & -3 \end{pmatrix} - \begin{pmatrix} -3 & 4 \\ -2 & 1 \end{pmatrix} = 0

To solve, we can rewrite this as: (2xxx3)=(3421)\begin{pmatrix} 2x & x \\ x & -3 \end{pmatrix} = \begin{pmatrix} -3 & 4 \\ -2 & 1 \end{pmatrix}

Equate corresponding elements:

  1. 2x=32x = -3
  2. x=4x = 4
  3. x=2x = -2
  4. 3=1-3 = 1 (inconsistent)

From these, we can see that there is inconsistency, so we’ll re-evaluate based on additional matrix operations if needed.


Problem 2

(x+142xx)=(665x)\begin{pmatrix} x+1 & 4 \\ 2x & x \end{pmatrix} = \begin{pmatrix} 6 & -6 \\ 5 & x \end{pmatrix}

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Math Problem Analysis

Mathematical Concepts

Matrix Equations
Algebra
System of Linear Equations

Formulas

Matrix equality: if \( A = B \), then corresponding elements of matrices A and B are equal.
Solving linear equations to find values of x.

Theorems

Matrix equality property

Suitable Grade Level

Grades 10-12