https://file.aiquickdraw.com/mathbot/file/1726544428981jlspdy4w.jpg

The problem asks to calculate the values of \( x \) and \( y \), given a matrix expression:

\[
\left( \frac{x \ 1}{1 \ x - x} \right) + \left( \frac{x \ 2}{2 \ 1} \right) = \left( \frac{4 \ 3}{1 \ 3} \right)
\]

The equation involves the addition of two 2x2 matrices on the left-hand side, equating to another 2x2 matrix on the right-hand side.

Let’s break it down:

1. **Left-hand side matrix:**

   \[
   \left( \frac{x \ 1}{1 \ x - x} \right) + \left( \frac{x \ 2}{2 \ 1} \right)
   \]
   This results in:
   \[
   \left( \frac{2x \ 3}{3 \ 1} \right)
   \]

2. **Equating to the right-hand side matrix:**

   \[
   \left( \frac{4 \ 3}{1 \ 3} \right)
   \]

Now, compare each corresponding element from the two matrices:

- For the first element: \( 2x = 4 \), so \( x = 2 \)
- For the second element: \( 3 = 3 \) (which holds true)
- For the third element: \( 3 = 1 \) (which holds true)
- For the fourth element: \( 1 = 3 \)

Hitunglah nilai x dan y jika ( (x 1)/(1 x-x) ) + ( (x 2)/(2 1) ) = ( (4 3)/(1 3) )

This problem involves solving for x and y in a matrix addition equation. It covers algebraic manipulation of 2x2 matrices, including matrix addition and solving systems of equations. Ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation