Question:

The system of equations
–kx + 3y – 14z = 25
–15x + 4y – kz = 3
–4x + y + 3z = 4
is consistent for all k in the set

Updated On: Oct 19, 2024

R
R – {–11, 13}
R – {13}
R – {–11, 11}

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The Correct Option is A

Solution and Explanation

The correct option is(D): R – {–11, 11}.

The system may be inconsistent if

Hence if system is consistent then

K∈R−{11,−11}

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Concepts Used:

Operations on Sets

Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:

1. Union of Sets:

The union of sets lists the elements in set A and set B or the elements in both set A and set B.
For example, {3,4} ∪ {1, 4} = {1, 3, 4}
It is denoted as “A U B”

2. Intersection of Sets:

Intersection of sets lists the common elements in set A and B.
For example, {3,4} ∪ {1, 4} = {4}
It is denoted as “A ∩ B”

3.Set Difference:

Set difference is the list of elements in set A which is not present in set B
For example, {3,4} - {1, 4} = {3}
It is denoted as “A - B”

4.Set Complement:

The set complement is the list of all elements present in the Universal set except the elements present in set A
It is denoted as “U-A”

The system of equations–kx + 3y – 14z = 25–15x + 4y – kz = 3–4x + y + 3z = 4is consistent for all k in the set