Given the system of linear equations: x + y/2 = 9 3x + y = 10 The value of the…
2006
Given the system of linear equations:
x + y/2 = 9
3x + y = 10
The value of the Frobenius norm for the above system of equations, in the normalized iterative form, is:
- A.
0.5
- B.
0.75
- C.
1.5
- D.
2.0
Attempted by 2 students.
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Correct answer: D
Rearrange the equations so that the diagonal coefficient of each equation is 1:
From 3x + y = 10:
x = 10/3 - y/3.
From x + y/2 = 9, multiply by 2:
2x + y = 18,
y = 18 - 2x.
So the off-diagonal coefficients in the normalized iterative form are -1/3 and -2. The corresponding iteration-coefficient matrix has entries:
[[0, -1/3], [-2, 0]].
The Frobenius norm is:
||B||F = √(0² + (-1/3)² + (-2)² + 0²)
= √(1/9 + 4)
= √(37/9)
≈ 2.03.
Among the given options, this is 2.0.