https://file.aiquickdraw.com/mathbot/file/17273127754196b3u2rf5.jpg

The problem is asking to solve for the values of \( x \) and \( y \) given two matrices \( A \) and \( B \) under the condition that matrix \( A \) is equal to the transpose of matrix \( B \), i.e., \( A = B^T \).

Given:
\[
A = \begin{pmatrix} x - 1 & -8 \\ 7 & 6 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 7 \\ -8 & x - y \end{pmatrix}
\]

Since \( A = B^T \), we know that the transpose of matrix \( B \) is:

\[
B^T = \begin{pmatrix} 3 & -8 \\ 7 & x - y \end{pmatrix}
\]

Now, equating matrix \( A \) and matrix \( B^T \), we get the following system of equations by comparing corresponding elements:

1. \( x - 1 = 3 \)
2. \( -8 = -8 \) (this is automatically satisfied)
3. \( 7 = 7 \) (this is automatically satisfied)
4. \( 6 = x - y \)

### Solving the system:

1. From the first equation \( x - 1 = 3 \), solving for \( x \):
   \[
   x = 3 + 1 = 4
   \]

2. Substituting \( x = 4 \) into the fourth equation \( 6 = x - y \):
   \[
   6 = 4 - y
   \]
   Solving for \( y \):
   \[
   y = 4 - 6 = -2
   \]

Thus, the values of \( x \) and \( y \) are \( x = 4 \) and \( y = -2 \).

Would you like further details or clarifications? Here are some related questions:

1. How do you find the transpose of a matrix?
2. What are the conditions for two matrices to be equal?
3. How can you verify if the solution for \( x \) and \( y \) is correct?
4. What are some common properties of matrix transposition?
5. Can this method be applied to any size of matrices?

**Tip:** Always double-check the dimensions and positions of elements when working with matrix transposition to avoid errors.

Diketahui matriks A = (x-1  -8 / 7 6) dan B = (3 7 / -8 x-y). Jika matriks A = B^T, maka nilai x dan y adalah?

Learn how to solve for x and y in the matrix equation A = B^T, where A and B are given matrices. This problem involves key concepts such as matrix transposition and equality, and is suitable for high school students studying linear algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation