JEE Exam > JEE Questions > In a third order determinant, each element of...
Start Learning for Free
In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value
- a)1
- b)9
- c)24
- d)16
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a third order determinant, each element of the first column consist...
N = 2 ×3 × 4 = 24.
Most Upvoted Answer
In a third order determinant, each element of the first column consist...
**Given information:**
- Each element of the first column consists of the sum of two terms.
- Each element of the second column consists of the sum of three terms.
- Each element of the third column consists of the sum of four terms.
**To find:**
The number of determinants in which the given third-order determinant can be decomposed.
**Solution:**
Let's denote the given third-order determinant as D.
D = |a1 b1 c1|
|a2 b2 c2|
|a3 b3 c3|
Since each element of the first column consists of the sum of two terms, we can write:
a1 = p + q,
a2 = r + s,
a3 = t + u,
Similarly, for the second and third columns, we have:
b1 = v + w + x,
b2 = y + z + p,
b3 = q + r + s,
c1 = t + u + v + w,
c2 = x + y + z + p,
c3 = q + r + s + t.
Now, let's expand the determinant D using the first row:
D = a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - a3b2)
Expanding each term, we get:
D = (p + q)(y + z + p)(q + r + s + t) - (v + w + x)(r + s)(q + r + s + t) + (t + u + v + w)(r + s)(q + r + s + t)
Now, let's simplify this expression:
D = (p + q)(y + z + p)(q + r + s + t) - (v + w + x)(r + s)(q + r + s + t) + (t + u + v + w)(r + s)(q + r + s + t)
Distributing the terms, we get:
D = pq(y + z + p)(q + r + s + t) + p(y + z + p)(r + s)(q + r + s + t) + (v + w + x)(r + s)(q + r + s + t)(q + r + s + t) + (t + u + v + w)(r + s)(q + r + s + t)
Now, we can see that D can be decomposed into several determinants, each containing only one term.
The total number of terms in the expanded expression is 2 * 3 * 4 = 24, which means that D can be decomposed into 24 determinants.
Therefore, the correct answer is option **C) 24**.
- Each element of the first column consists of the sum of two terms.
- Each element of the second column consists of the sum of three terms.
- Each element of the third column consists of the sum of four terms.
**To find:**
The number of determinants in which the given third-order determinant can be decomposed.
**Solution:**
Let's denote the given third-order determinant as D.
D = |a1 b1 c1|
|a2 b2 c2|
|a3 b3 c3|
Since each element of the first column consists of the sum of two terms, we can write:
a1 = p + q,
a2 = r + s,
a3 = t + u,
Similarly, for the second and third columns, we have:
b1 = v + w + x,
b2 = y + z + p,
b3 = q + r + s,
c1 = t + u + v + w,
c2 = x + y + z + p,
c3 = q + r + s + t.
Now, let's expand the determinant D using the first row:
D = a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - a3b2)
Expanding each term, we get:
D = (p + q)(y + z + p)(q + r + s + t) - (v + w + x)(r + s)(q + r + s + t) + (t + u + v + w)(r + s)(q + r + s + t)
Now, let's simplify this expression:
D = (p + q)(y + z + p)(q + r + s + t) - (v + w + x)(r + s)(q + r + s + t) + (t + u + v + w)(r + s)(q + r + s + t)
Distributing the terms, we get:
D = pq(y + z + p)(q + r + s + t) + p(y + z + p)(r + s)(q + r + s + t) + (v + w + x)(r + s)(q + r + s + t)(q + r + s + t) + (t + u + v + w)(r + s)(q + r + s + t)
Now, we can see that D can be decomposed into several determinants, each containing only one term.
The total number of terms in the expanded expression is 2 * 3 * 4 = 24, which means that D can be decomposed into 24 determinants.
Therefore, the correct answer is option **C) 24**.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer?
Question Description
In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer?.
In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer?.
Solutions for In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has valuea)1b)9c)24d)16Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup