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Q8:
If $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} 6 & 2 \\ 18 & 6 \end{vmatrix}$, then $x$ is equal to
Solution :
Step 1: Evaluation of the Determinants
To solve for the unknown variable $x$, we must apply the definition of a $2 \times 2$ determinant. For any matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, the determinant is given by $|A| = ad - bc$ [Definition of Determinant for $2 \times 2$ matrices].
For the Left-Hand Side (LHS):
$\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = (x)(x) - (18)(2)$
$= x^2 - 36$ [Algebraic simplification]
For the Right-Hand Side (RHS):
$\begin{vmatrix} 6 & 2 \\ 18 & 6 \end{vmatrix} = (6)(6) - (18)(2)$
$= 36 - 36$
$= 0$
Step 2: Constructing the Algebraic Equation
Equating the results from Step 1 as per the problem statement:
$x^2 - 36 = 0$
Step 3: Solving for $x$
To isolate $x$, we apply the addition property of equality:
$x^2 = 36$
Taking the square root on both sides requires considering both positive and negative roots [Principle of Square Roots]:
$x = \pm \sqrt{36}$
$x = \pm 6$
Visual Representation
Step 4: Verification
| Value of $x$ | Calculation | Result |
|---|---|---|
| $6$ | $6^2 - 36$ | $0$ |
| $-6$ | $(-6)^2 - 36$ | $0$ |
Final Solution: $x = \pm 6$
More Questions from Class 12 Mathematics Determinants EXERCISE 4.1
- Q1: Evaluate the determinant: $\begin{vmatrix} 2 & 4 \\ -5 & -1 \end{vmatrix}$
- Q2(i): Evaluate the determinant: (i) $\begin{vmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{vmatrix}$
- Q2(ii): Evaluate the determinant: (ii) $\begin{vmatrix} x^2 - x + 1 & x - 1 \\ x + 1 & x + 1 \end{vmatrix}$
- Q3: If A = $\begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix}$, then show that $| 2A | = 4 | A |$
- Q4: If A = $\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{bmatrix}$, then show that $| 3 A | = 27 | A |$
- Q5(i): Evaluate the determinant: (i) $\begin{vmatrix} 3 & -1 & -2 \\ 0 & 0 & -1 \\ 3 & -5 & 0 \end{vmatrix}$
- Q5(ii): Evaluate the determinant: (ii) $\begin{vmatrix} 3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1 \end{vmatrix}$
- Q5(iii): Evaluate the determinant: (iii) $\begin{vmatrix} 0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0 \end{vmatrix}$
- Q5(iv): Evaluate the determinant: (iv) $\begin{vmatrix} 2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0 \end{vmatrix}$
- Q6: If A = $\begin{bmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{bmatrix}$, find $| A |$
- Q7(i): Find values of $x$, if (i) $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$
- Q7(ii): Find values of $x$, if (ii) $\begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} = \begin{vmatrix} x & 3 \\ 2x & 5 \end{vmatrix}$
CBSE Solutions for Class 12 Mathematics Determinants
Chapters in CBSE - Class 12 Mathematics
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Taj Bagh, Nagpur
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I have twelve years of experience in teaching mathematics. I hold a B.Tech in Mechanical Engineering and an M.Tech in Mechanical Engineering Design. One of my most rewarding experiences as a teacher was when I helped a student who was depressed due to poor math grades. The student's parents approached me for help, and after taking classes from me, she cleared her tenth board exam with excellent marks in math. My main passion is to teach the basics of the subject, as I've noticed that many students need more foundational knowledge and help with math. I teach Mathematics for classes eighth to twelfth through UrbanPro, both online and offline, in individual and group settings. However, my primary focus is on teaching twelfth-class students. I take great care in designing my lesson plans, ensuring students have a solid understanding of the fundamentals before moving on to more complex topics. During my classes, I use a whiteboard to visually explain concepts and engage students in an interactive learning experience. My teaching philosophy revolves around providing a strong foundation in mathematics. A solid understanding of the basics is crucial for students to excel in the subject. I am patient and understanding towards students who may struggle with math, and I employ various teaching techniques to cater to different learning styles. I need to create a positive and supportive learning environment where students feel comfortable asking questions and seeking clarification. My expertise in mechanical engineering adds dimension to my teaching, as I can provide real-world applications of mathematical concepts, making the subject more relevant and exciting for students. I am passionate about inspiring a love for mathematics in my students and helping them build confidence in their math skills. My focus on teaching the basics, creating a positive learning environment, and providing real-world applications of mathematical concepts, makes me an effective and successful teacher.
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Dilshad Garden, Delhi
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I have been teaching students of Class 12th for the last 20 years. I clear the concepts hidden behind difficult expressions authored in poems or chapters, relating them to practicality, and impart impressive writing skills. Many of my students have scored more than 90% marks in board exams. My accomplishments: - I have authored and edited many school books, novels, books of post graduate level, competition books, and other English content. - My work gets circulated abroad and all across India. - Certificate course in English language from Harvard University(US). - TOEFL score by EFSET- 8 band -I am graduate in science from Hindu College, Delhi University. - I am an MBA (HRD). - I treasure wonderful reviews of my students in my UrbanPro profile. - English Test conducted by Upwork (US) - 4:40/4.10 out of 5 by people per hour (US) - 88% - I also take classes for Spoken English, IELTS/TOEFL, competitions, content writing, and classes from 8th to 12th (English Subject).
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L. B. Nagar Chandrapuri Colony, Hyderabad
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Taught the same course for the Ministry of Education of in a country called Brunei Darussalam. After relocated to India I had been teaching in BHAT'S CLASSES, BANGALORE before the pandemic for both CBSE/ICSE & the STATE SYLLABI.
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Kushaiguda, Hyderabad
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