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Let S be the set of all column matrices such that b1, b2, bε R and the system of equations (in real variables)
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each 
  • a)
    x + 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?
Verified Answer
Let S be the set of all column matricessuch that b1, b2, b3ε R...
as planes are non parallel is must represent family of planes for solution to exist 
Must be 2x + b + 3z + b3 = 0 which gives μ = 1, b1 + b2 + 3b3 = 0 which is not true always
 
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Let S be the set of all column matricessuch that b1, b2, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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, b3ε Rand the system of equations (in real variables)has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least onesolution for eacha)x + 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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