If
\[
\begin{bmatrix} 1 & 3 & 1 \\ k & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix}
\]
has a determinant of \( \pm 6 \), then the value of \( k \) is:
Show Hint
- \( 1 \)
- \( -2 \)
- \( 2 \)
- \( \pm 2 \)
The Correct Option is D
Solution and Explanation
The determinant is:
\[ \det = 1 \cdot \begin{vmatrix} 0 & 1 \\ 0 & 1 \end{vmatrix} - 3 \cdot \begin{vmatrix} k & 1 \\ 1 & 1 \end{vmatrix} + 1 \cdot \begin{vmatrix} k & 0 \\ 1 & 0 \end{vmatrix}. \]Simplify:
\[ \det = 0 - 3(k - 1) + k = -3k + 3 + k = -2k + 3. \]Given \( |\det| = 6 \), solve:
\[ -2k + 3 = \pm 6 \quad \Rightarrow \quad k = \pm 2. \] Final Answer: \( \boxed{\pm 2} \)Top Questions on Matrix
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A scholarship is a sum of money provided to a student to help him or her pay for education. Some students are granted scholarships based on their academic achievements, while others are rewarded based on their financial needs.
Every year, a school offers scholarships to girl children and meritorious achievers based on certain criteria. In the session 2022–23, the school offered a monthly scholarship of ₹3,000 each to some girl students and ₹4,000 each to meritorious achievers in academics as well as sports.
In all, 50 students were given the scholarships, and the monthly expenditure incurred by the school on scholarships was ₹1,80,000.
Based on the above information, answer the following questions:
(i) Express the given information algebraically using matrices.
(ii) Check whether the system of matrix equations so obtained is consistent or not.
(iii)(a) Find the number of scholarships of each kind given by the school using matrices.
(iii)(b) Had the amount of scholarship given to each girl child and meritorious student been interchanged, what would be the monthly expenditure incurred by the school?
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China was able to control its rapid population growth rate owing to __________.
(Choose the correct alternative to fill in the blank):- CBSE CLASS XII - 2024
- Economic History
Modernization is an important economic planning objective that focuses on ___________.
(Choose the correct alternative to fill in the blank):
[(i)] Adoption of innovative technology
[(ii)] Equal distribution of income and wealth
[(iii)] Bringing positive changes in the social outlook- CBSE CLASS XII - 2024
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During the British rule, India’s foreign trade had various features except ________.
(Choose the correct alternative to fill in the blank):- CBSE CLASS XII - 2024
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The present day rapid industrial growth in China can be traced back to the economic reforms introduced in 1978, where _______.
(Choose the correct alternative to fill in the blank):
(i) Initially reforms were initiated in agriculture, foreign trade, and investment sectors.
(ii) The policy of dual pricing was adopted.
(iii) The Government revoked the policy of Special Economic Zones.- CBSE CLASS XII - 2024
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_______ farming is a system that is helpful in restoring, maintaining and enhancing the ecological balance.
(Choose the correct alternative to fill in the blank):- CBSE CLASS XII - 2024
- Indian Economy