Question

what you mean by unique solution​

Answer 1

Answer:

Step-by-step explanation:

In linear algebra whenever we deal with equations and expressions, we come across with a phrase "unique solution". By the term unique solution, one mean to say that only one specific solution set exists for a given equation. What this pretty much means is, depending upon how many equations we have, all the equations will intersect at one particular point.

So, if we have two equations, then unique solution will mean that there is one and only point at which the two equations intersect. Similarly, in case of three equations, the unique solution will be one point at which all three equations intersect all together. In other words, all three equations will intersect at one particular point, called unique solution. If we have more equations than that, then again the unique solution would refer to a certain point where all the equations will intersect. It looks bit complex, but this is the beauty of a unique solution concept.

Examples:

Problem 1:

Solve the linear algebraic equation 5x - 12 = 18 and find its unique solution

Solution:

Given equation is 5x - 12 = 18

Add 12 on both the sides of the equation, we get

5x = 30

Divide the above equation by 5 on both the sides, we get

x = 6

The unique solution is x = 6

Answer:

The final answer is x = 6.

Problem 2:

Solve the linear algebraic equation 17x + 34 = 46 and find its unique solution

Solution:

Given equation is 17x + 34 = 46

Subtract the above equation by 34 on both the sides, we get

17x = 12

Divide the above equation by 17 on both the sides, we get

x = 1217

The unique solution is x = 1217

Answer:

The final answer is x = 1217.

Answer 2

A unique solution in linear equations is defined as when the system is consistent and its determinant is non-zero.

• A unique solution in linear equations is defined as when the system is consistent and its determinant is non-zero.A unique solution exists if and only if,
• A unique solution in linear equations is defined as when the system is consistent and its determinant is non-zero.A unique solution exists if and only if,All equations are consistent
• A unique solution in linear equations is defined as when the system is consistent and its determinant is non-zero.A unique solution exists if and only if,All equations are consistentAll ll equations are independent
• A unique solution in linear equations is defined as when the system is consistent and its determinant is non-zero.A unique solution exists if and only if,All equations are consistentAll ll equations are independentThe number of unknowns and the number of equations is equal.

It means that only one specific solution set exists for a given equation. All the equations will intersect at one particular point. In case of three equations, the unique solution will be one point at which all three equations intersect all together. If we have n equations the unique solution will be one point at which all three equations intersect all together.

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