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by Himanshu Garg
written by Himanshu Garg

If \( \left| \begin{matrix} 2x & 5 \\ 1 & 3 \end{matrix} \right| = 8 \), write the value of \( x \).

Question 5: If

2x5
13

= 8, find the value of \( x \).

SHOW ANSWER
Answer: The value of \( x \) is \( \frac{13}{6} \).

Solution:
1. Compute the determinant:

2x5
13

= (2x × 3) − (5 × 1) = 6x − 5

2. Set the determinant equal to 8:

6x − 5 = 8

3. Solve for \( x \):

6x = 13 ⇒ x = 13/6

Thus, \( x = \frac{13}{6} \).

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Experienced Engineering Mentor and Educator | Empowering Students to Excel. With a passion for guiding and empowering engineering students, I am dedicated to supporting their academic journey and fostering their success. With a strong background in Process Control (instrumentation), I completed my Mtech in 2020. Passionate about helping students excel, aims to introduce new modules addressing mental stress problems and other crucial areas in Engineer's Planet. Connect with me to explore opportunities for collaboration and support in engineering education.

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