Let S be the set of all column matricessuch that b1, b2, b3 andisin; R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and andminus;2x andminus; yandminus;3z = b3c)andminus;x + 2y +5z = b1, 2x andminus; 4y +10z = b2 and x andminus; 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y andminus;5z = b3Correct answer is option 'A,D'. Can you explain this answer?

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JEE Exam > JEE Questions > Let S be the set of all column matricessuch t...

Let S be the set of all column matrices

such that b₁, b₂, b₃ ∈ R and the system of equations (in real variables)
-x + 2y + 5z = b₁
2x - 4y + 3z = b₂
x - 2y + 2z = b₃
Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each

a)
a + 2y +3z = b₁, 4y +5z = b₂ and x + 2y +6z = b₃
b)
x + y+3z = b₁, 5x +2y +6z = b₂ and −2x − y−3z = b₃
c)
−x + 2y +5z = b₁, 2x − 4y +10z = b₂ and x − 2y + 5z = b₃
d)
x + 2y +5z = b₁, 2x +3z = b₂ and x + 4y −5z = b₃

Correct answer is option 'A,D'. Can you explain this answer?

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Let S be the set of all column matricessuch that b1, b2, b3 ∈ R a...

The condition for at least one solution is as follows.

...(1)
(A) The determinant of the equation is given as,
∆≠ 0
Therefore, the equations have a unique solution.
Hence, option (A) is correct. (B) The determinant of the equation is calculated as,

The value of ∆₁ is also zero.
The condition for infinite solution is that ∆₂ and ∆₃ must be equal to zero.

From the above equation it can be concluded, that the values will not satisfy the equation (1).
Hence, option (B) is wrong. (C) The determinant of the equation is given as, ∆= 0
Therefore, the equations of the plane represents that the planes are parallel to each other.
The relationship between b₁,b₂ and b₃ is given as,

It is clear from the above relationship, that the values will not satisfy the equation (1).
Hence, option (C) is wrong. (D) The determinant of the equation is as follows. ∆≠ 0
Thus, the equations have a unique solution.
Hence, option (D) is correct.
Hence, option (A) and option (D) are correct.

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Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer?

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Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer?.

Solutions for Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. 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 Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer?, a detailed solution for Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer? has been provided alongside types of Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let S be the set of all column matricessuch that b1, b2, b3 ∈ R and the system of equations (in real variables)-x + 2y + 5z = b12x - 4y + 3z = b2x - 2y + 2z = b3Has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for eacha)a + 2y +3z = b1, 4y +5z = b2 and x + 2y +6z = b3b)x + y+3z = b1, 5x +2y +6z = b2 and −2x − y−3z = b3c)−x + 2y +5z = b1, 2x − 4y +10z = b2 and x − 2y + 5z = b3d)x + 2y +5z = b1, 2x +3z = b2 and x + 4y −5z = b3Correct answer is option 'A,D'. Can you explain this answer? tests, examples and also practice JEE tests.

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