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Find the difference between the sum of (x + y + z) and the Trace upper triangular matrix formed by using the gauss elimination method.
- a)6
- b)8
- c)10
- d)12
Correct answer is option 'C'. Can you explain this answer?
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Find the difference between the sum of (x + y + z) and the Trace upper...
Concept:
Gauss elimination method,
In this method, an augmented matrix is formed by the coefficient of x, y, & z then,
By using row transformation, it is converted into an upper triangular matrix.
Calculation:
AX = B
R2 → R2 - 2R1
R3 → R3 - R1
R3 → R3 + R2
Now, again converting this matrix into equation,
x + 3y + 2z = 5
-2y - 10z = -14
-9z = -9
on solving
z= 1, y = 2 & x = -3
x + y + z = -3 + 2 + 1 = 0
Trace of upper traingular matrix = 1 - 2 - 9 = -10
Difference = ( x + y + z ) - trace = 0- (-10 =)
Difference = 10
Gauss elimination method,
In this method, an augmented matrix is formed by the coefficient of x, y, & z then,
By using row transformation, it is converted into an upper triangular matrix.
Calculation:
AX = B
R2 → R2 - 2R1
R3 → R3 - R1
R3 → R3 + R2
Now, again converting this matrix into equation,
x + 3y + 2z = 5
-2y - 10z = -14
-9z = -9
on solving
z= 1, y = 2 & x = -3
x + y + z = -3 + 2 + 1 = 0
Trace of upper traingular matrix = 1 - 2 - 9 = -10
Difference = ( x + y + z ) - trace = 0- (-10 =)
Difference = 10
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Find the difference between the sum of (x + y + z) and the Trace upper triangular matrix formed by using the gauss elimination method.a)6b)8c)10d)12Correct answer is option 'C'. Can you explain this answer?
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