Question

what is unique solution, no solution, infinite solution​

Answer 1

Step-by-step explanation:

Unique Solution

The example shown previously in this module had a unique solution. The structure of the row reduced matrix was

∣∣∣∣∣100110−1−51|||58−1∣∣∣∣∣

and the solution was

x=1

y=3

z=−1

As you can see, each variable in the matrix can have only one possible value, and this is how you know that this matrix has one unique solution

No solution

Let’s suppose you have a system of linear equations that consist of:

x+y+z=2

y−3z=1

2x+y+5z=0

The augmented matrix is

∣∣∣∣∣1021111−35|||210∣∣∣∣∣

and the row reduced matrix is

∣∣∣∣∣1000104−30|||11−3∣∣∣∣∣

As you can see, the final row states that

0x+0y+0z=−3

which impossible, 0 cannot equal -3. Therefore this system of linear equations has no solution.

Infinite Solutions¶

Let’s suppose you have a system of linear equations that consist of:

−3x−5y+36z=10

−x+7z=5

x+y−10z=−4

The augmented matrix is

∣∣∣∣∣−3−11−501367−10|||105−4∣∣∣∣∣

and the row reduced matrix is

∣∣∣∣∣100020−7−30|||−510∣∣∣∣∣

As you can see, the final row of the row reduced matrix consists of 0. This means that for any value of Z, there will be a unique solution of x and y, therefore this system of linear equations has infinite solutions.

Answer 2

Step-by-step explanation:

A solution is a homogeneous mixture of two or more substances. ... The solute is the substance that is dissolved in the solvent. The amount of solute that can be dissolved in solvent is called its solubility. For example, in a saline solution, salt is the solute dissolved in water as the solvent.