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Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.
If the system of equations x - ky - z = 0,
kx - y - z = 0,
x + y - z = 0
has a non-zero solution, then possible values of k are ±A. Calculate the value of A.
Correct answer is '1'. Can you explain this answer?
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Most Upvoted Answer
Directions: The answer to the following question is a single-digit i...
Since the given system has non-zero solution, therefore
Applying C1 → C1 - C2, C2 → C2 + C3
⇒ 2(k + 1) - (k + 1)2 = 0
⇒ (k + 1) (2 - k - 1) = 0
⇒ k = ± 1
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Directions: The answer to the following question is a single-digit i...
Given:
The system of equations is:
x - ky - z = 0
kx - y - z = 0
x + y - z = 0
To Find:
Possible values of k.
Solution:
To find the possible values of k, we need to solve the system of equations.
Step 1: Add the first and second equations to eliminate z:
(x - ky - z) + (kx - y - z) = 0
x - ky + kx - y - 2z = 0
(x + kx) + (-y - ky) - 2z = 0
(x(1 + k) - y(1 + k)) - 2z = 0
(x - y)(1 + k) - 2z = 0
Step 2: Substitute the third equation into the above expression:
(x - y)(1 + k) - 2(x + y) = 0
(x - y - 2x - 2y)(1 + k) = 0
(-x - 3y)(1 + k) = 0
Step 3: Set each factor equal to zero:
-x - 3y = 0 ...(1 + k) = 0
Step 4: Solve equation (1) for x:
x = -3y
Step 5: Substitute the value of x into the third equation:
-3y + y - z = 0
-2y - z = 0
z = -2y
Step 6: Substitute the values of x and z into the first equation:
x - ky - z = 0
-3y - ky + 2y = 0
-ky - y = 0
y(-k - 1) = 0
Step 7: Set each factor equal to zero:
y = 0 or -k - 1 = 0
Step 8: Solve equation (2) for k:
-k - 1 = 0
k = -1
Step 9: Therefore, the possible value of k is -1.
Answer:
The value of A is 1.
The system of equations is:
x - ky - z = 0
kx - y - z = 0
x + y - z = 0
To Find:
Possible values of k.
Solution:
To find the possible values of k, we need to solve the system of equations.
Step 1: Add the first and second equations to eliminate z:
(x - ky - z) + (kx - y - z) = 0
x - ky + kx - y - 2z = 0
(x + kx) + (-y - ky) - 2z = 0
(x(1 + k) - y(1 + k)) - 2z = 0
(x - y)(1 + k) - 2z = 0
Step 2: Substitute the third equation into the above expression:
(x - y)(1 + k) - 2(x + y) = 0
(x - y - 2x - 2y)(1 + k) = 0
(-x - 3y)(1 + k) = 0
Step 3: Set each factor equal to zero:
-x - 3y = 0 ...(1 + k) = 0
Step 4: Solve equation (1) for x:
x = -3y
Step 5: Substitute the value of x into the third equation:
-3y + y - z = 0
-2y - z = 0
z = -2y
Step 6: Substitute the values of x and z into the first equation:
x - ky - z = 0
-3y - ky + 2y = 0
-ky - y = 0
y(-k - 1) = 0
Step 7: Set each factor equal to zero:
y = 0 or -k - 1 = 0
Step 8: Solve equation (2) for k:
-k - 1 = 0
k = -1
Step 9: Therefore, the possible value of k is -1.
Answer:
The value of A is 1.
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Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.If the system of equations x - ky - z = 0,kx - y - z = 0,x + y - z = 0has a non-zero solution, then possible values of k are ±A. Calculate the value of A.Correct answer is '1'. Can you explain this answer?
Question Description
Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.If the system of equations x - ky - z = 0,kx - y - z = 0,x + y - z = 0has a non-zero solution, then possible values of k are ±A. Calculate the value of A.Correct answer is '1'. 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 Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.If the system of equations x - ky - z = 0,kx - y - z = 0,x + y - z = 0has a non-zero solution, then possible values of k are ±A. Calculate the value of A.Correct answer is '1'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.If the system of equations x - ky - z = 0,kx - y - z = 0,x + y - z = 0has a non-zero solution, then possible values of k are ±A. Calculate the value of A.Correct answer is '1'. Can you explain this answer?.
Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.If the system of equations x - ky - z = 0,kx - y - z = 0,x + y - z = 0has a non-zero solution, then possible values of k are ±A. Calculate the value of A.Correct answer is '1'. 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 Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.If the system of equations x - ky - z = 0,kx - y - z = 0,x + y - z = 0has a non-zero solution, then possible values of k are ±A. Calculate the value of A.Correct answer is '1'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to the following question is a single-digit integer ranging from 0 to 9.If the system of equations x - ky - z = 0,kx - y - z = 0,x + y - z = 0has a non-zero solution, then possible values of k are ±A. Calculate the value of A.Correct answer is '1'. Can you explain this answer?.
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