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If the system of equations αx + 3y + 5z = 0, 2x - 4αy + αz = 0, -4x + 18y + 7z = 0 has infinite number of solutions, then the value of α is
  • a)
    1,-3    
  • b)
    -1.3    
  • c)
    1,3    
  • d)
    -1,-3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the system of equations αx + 3y + 5z = 0, 2x - 4αy + ^...
System AX = 0 has infinite number of solutions, then |A| = 0
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Most Upvoted Answer
If the system of equations αx + 3y + 5z = 0, 2x - 4αy + ^...
To determine the solution to the given system of equations, we can use the method of elimination or substitution. However, since the given system has an infinite number of solutions, it implies that the equations are dependent and can be rewritten as multiples of each other.

Let's analyze the given system of equations:

Equation 1: x + 3y + 5z = 0
Equation 2: 2x - 4y + z = 0
Equation 3: -4x + 18y + 7z = 0

Since the equations are dependent, we can find a scalar value 'k' such that one equation is a multiple of another equation. Let's express Equation 2 and Equation 3 in terms of Equation 1:

Equation 2: 2x - 4y + z = 0
Multiplying Equation 1 by 2:
2(x + 3y + 5z) = 0
2x + 6y + 10z = 0

Comparing Equation 2 and the new equation:
2x - 4y + z = 2x + 6y + 10z

Simplifying:
-10y - 9z = 0

Equation 3: -4x + 18y + 7z = 0
Multiplying Equation 1 by -4:
-4(x + 3y + 5z) = 0
-4x - 12y - 20z = 0

Comparing Equation 3 and the new equation:
-4x + 18y + 7z = -4x - 12y - 20z

Simplifying:
30y + 27z = 0

Now we have two equations in terms of Equation 1:

-10y - 9z = 0
30y + 27z = 0

If we divide the second equation by 3, we get:

10y + 9z = 0

Comparing this equation with the first equation we obtained, we can see that they are identical. This means that any values of y and z that satisfy -10y - 9z = 0 will also satisfy 10y + 9z = 0.

The equation -10y - 9z = 0 represents a line in the yz-plane. Since the system has an infinite number of solutions, any point on this line will satisfy the original system of equations.

Hence, the correct answer is option 'A' which represents the solution (1, -3).
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If the system of equations αx + 3y + 5z = 0, 2x - 4αy + αz = 0, -4x + 18y + 7z = 0 has infinite number of solutions, then the value of αisa)1,-3 b)-1.3 c)1,3 d)-1,-3Correct answer is option 'A'. Can you explain this answer?
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