Consider the system of equationsThe value of x3(round off to the nearest integer), is ______.Correct answer is '3'. Can you explain this answer?

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Consider the system of equations

The value of x₃ (round off to the nearest integer), is ______.

Correct answer is '3'. Can you explain this answer?

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Consider the system of equationsThe value of x3(round off to the neare...

The given system has 4 equations and 3 unknowns.

Hence it is a over-determined system of equations.

The equations are;

x₁ + 3x₂ + 2x₃ = 1 --(1)

2x₁ + 2x₂ - 3x₃ = 1 ---(2)

4x₁ + 4x₂ - 6x₃ = 2 ---(3)

2x₁ + 5x₂ + 2x₃ = 1 ---(4)

Note that equation (2) and (3) are linearly dependent on each other and equation 3 is twice that of equation (2).

Hence considering equation 1, 2 and 4 -

⇒ x₃ = 3

Important Points:

Under-determined system: Number of equations < Number of unknowns
Over-Determined system: Number of equation > Number of unknowns
Equally Determined system: Number of equation = Number of unknowns

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Consider the system of equationsThe value of x3(round off to the neare...

The given system has 4 equations and 3 unknowns.

Hence it is a over-determined system of equations.

The equations are;

x₁ + 3x₂ + 2x₃ = 1 --(1)

2x₁ + 2x₂ - 3x₃ = 1 ---(2)

4x₁ + 4x₂ - 6x₃ = 2 ---(3)

2x₁ + 5x₂ + 2x₃ = 1 ---(4)

Note that equation (2) and (3) are linearly dependent on each other and equation 3 is twice that of equation (2).

Hence considering equation 1, 2 and 4 -

⇒ x₃ = 3

Important Points:

Under-determined system: Number of equations < Number of unknowns
Over-Determined system: Number of equation > Number of unknowns
Equally Determined system: Number of equation = Number of unknowns

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