Math Problem Statement

Find all values of m so that the system of linear equations has only one solution: x + y + 3z = 1 -x + 3y + 2z = 3 3x - y + 4z = m

Solution

It looks like you've uploaded an image. Let me take a look at it and extract the relevant details for you. PIL import Image

image_path = '/mnt/data/1733704981711a04lgtww.jpg' image = Image.open(image_path)

image.show()I have displayed the image you uploaded. I will now analyze its contents to extract the relevant mathematical information. pytesseract

extracted_text = pytesseract.image_to_string(image)

extracted_textThe image contains the following mathematical system:

a + yrs &= 1 \\ -c + 3y + 22 &= 3 \\ Br - yy + 42 &= Mm \end{aligned}$$ The problem asks for the values of $$m$$ that make this system have only one solution. However, the equations appear a bit unclear, with some unusual notations and potential errors in transcription. If you could clarify the variables or correct any typos, I can proceed with solving the system properly. Would you like to provide more context or revise the equations?

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Linear Algebra
Systems of Linear Equations
Determinants

Determinant of a 3x3 matrix: det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)
Criteria for unique solutions: det(A) ≠ 0

Cramer's Rule
Rank Theorem

Grades 10-12

Determine Unique Solutions for a System of Equations with Parameter m

Solving Systems of Linear Equations with Parameters a, b, c for Unique, Infinite, or No Solutions

Determinant Calculation for Non-Trivial Solutions of a 3x3 System

Solving Systems of Linear Equations with a Unique, No, or Infinitely Many Solutions

Conditions for Solutions in a System of Linear Equations