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lorasvet [3.4K]
3 years ago
9

Determine if the linear system

Mathematics
1 answer:
zubka84 [21]3 years ago
4 0

Answer:

b. The system is not in echelon form because the system is not organized in descending "stair step" pattern so that the index of the leading variables increases from the top to bottom.

Step-by-step explanation:

The given linear system has a equation which is not in echelon form. The echelon is a system which divides the data into rigid hierarchal groups. The given linear equation in not in echelon form as the leading variables are increased from top to bottom indicating descending stair step pattern.

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\mathbf{X_E (2) =  1}

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Let E be the set of all even positive integers in the universe Z of integers,

i.e

E = {2,4,6,8,10 ....∞}

X_E : Z \to R be the characteristic function of E.

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X_E(x) = \left \{ {{1 \ if  \ x \ \  is \ an \ element \ of \ E} \atop {0 \ if  \ x \ \  is \ not \ an  \ element \ of \ E}} \right.

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\mathbf{X_E (-2) = 0 }   since  - 2 is less than 0 , and -2 is not an element of E

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x which is and element of Z such that X is also an element of x which is equal to 1.

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\{ x \in Z: X_E(x) = 1\} = \{ x \in Z | x \in E\} \\ \\  \mathbf{\{ x \in Z: X_E(x) = 1\}  = E}

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