https://file.aiquickdraw.com/mathbot/file/1726180363902pfyoeiy0.jpg

The problem asks us to find matrix \( X \) such that:

\[
X \begin{pmatrix} 4 & -7 \\ 3 & -5 \end{pmatrix} = \begin{pmatrix} -3 & 10 \\ 7 & 8 \end{pmatrix}
\]

To find matrix \( X \), we need to multiply both sides of the equation by the inverse of matrix:

\[
A = \begin{pmatrix} 4 & -7 \\ 3 & -5 \end{pmatrix}
\]

Thus,

\[
X = B A^{-1}
\]

where 

\[
B = \begin{pmatrix} -3 & 10 \\ 7 & 8 \end{pmatrix}
\]

To compute \( A^{-1} \), we'll use the formula for the inverse of a 2x2 matrix:

\[
A^{-1} = \frac{1}{\text{det}(A)} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}
\]

where \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \).

Let's calculate the inverse and find matrix \( X \).The matrix \( X \) that satisfies the equation is:

\[
X = \begin{pmatrix} -15 & 19 \\ -59 & 81 \end{pmatrix}
\]

Would you like further details or have any questions about the solution?

### Additional Related Questions:
1. How do you calculate the determinant of a 2x2 matrix?
2. What are some properties of matrix inverses?
3. How would this problem change if matrix \( A \) was not invertible?
4. Can you explain how matrix multiplication works?
5. What are some real-world applications of matrix inversion?

**Tip:** Understanding matrix operations such as multiplication and inversion is fundamental in linear algebra, which has applications in areas like computer graphics, machine learning, and engineering.

Tentukan matriks X yang memenuhi X * (4 -7 / 3 -5) = (-3 10 / 7 8)

Learn how to find matrix X that satisfies the equation involving matrix multiplication and inversion. This problem demonstrates key concepts in linear algebra, such as matrix multiplication and inversion. Suitable for college-level linear algebra students.

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