https://file.aiquickdraw.com/mathbot/file/1725856305482nosx41dj.jpg

ubahlah matriks berikut ke dalam bentuk matriks eselon baris dan matriks eselon baris tereduksi dengan menggunakan operasi baris elementer (OBE)

The matrices provided need to be converted into row echelon form (REF) and reduced row echelon form (RREF) using elementary row operations (EROs). Let's start by determining the REF and RREF for each matrix. Here are the matrices from the image:

1. \( \begin{bmatrix} 3 & 1 & 2 \\ 8 & -9 & 1 \end{bmatrix} \)
2. \( \begin{bmatrix} 1 & -1 & 1 \\ 1 & 2 & -1 \\ 1 & 1 & 1 \end{bmatrix} \)
3. \( \begin{bmatrix} 1 & -1 & 0 & 3 \\ 2 & 2 & 1 & 5 \end{bmatrix} \)

I'll begin by converting each of these matrices into REF and RREF forms. Starting with the first matrix:

### Matrix 1
- **Original**: \( \begin{bmatrix} 3 & 1 & 2 \\ 8 & -9 & 1 \end{bmatrix} \)

#### Row Echelon Form (REF)
- Divide the first row by 3 to make the leading entry a 1.
- Subtract \( \frac{8}{3} \) times the first row from the second row to make the entry below the leading 1 a 0.

#### Reduced Row Echelon Form (RREF)
- Continue from the REF form and make further adjustments to achieve the identity matrix where possible.

Let's calculate these forms now.

Ubahlah matriks berikut ke dalam bentuk matriks eselon baris dan matriks eselon baris tereduksi dengan menggunakan operasi baris elementer (OBE).

Learn how to convert given matrices into Row Echelon Form (REF) and Reduced Row Echelon Form (RREF) using elementary row operations (EROs). This step-by-step solution includes detailed explanations for understanding matrix transformations in linear algebra. Suitable for high school and college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation