Let me extract the mathematical content from the image and help you solve the problems step-by-step. Please hold on for a moment. PIL import Image import pytesseract

Load the image to extract text

image_path = "/mnt/data/1733875120808k1vsxzc3.jpg" image = Image.open(image_path)

Extract text from the image using pytesseract

extracted_text = pytesseract.image_to_string(image) extracted_textThe extracted text from the image is partially unclear. Let me reconstruct the mathematical problems based on the provided content and visible layout:

Questions

1. (4 points) What is the trace of the matrix $A = \begin{bmatrix} 4 & 1 \\ 0 & 3 \end{bmatrix}$?

   • (a) 8
   • (b) 12
   • (c) 7
   • (d) 4

2. (4 points) If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}$, what is $AB$? Options seem unclear; if you have specifics, let me know.

3. (4 points) If $A = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix}$ and the vector $v = \begin{bmatrix} -2 \\ 3 \end{bmatrix}$, what is $Av$?

4. (4 points) If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, what is the determinant of $A$?

   • (a) 10
   • (b) -2

Would you like me to start solving these problems? If so, let me know which one to begin with or if you'd like all of them addressed step-by-step!