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Although the vectors QR and RQ refer to the same segment between the points R and Q, they are two distinct vectors and can not be considered equivalent. It happens because a vector is characterized by both numerical value and vector's direction. Vectors QR and RQ have exactly the same length but opposite direction and, therefore, differ from each other.
Hi! It is simple, though unusual. Vectors differ from many other mathematical notions because a vector is determined by both numerical value and vector's direction. So, vector is not only a number. You can imagine a vector as an arrow of certain length.
Exactly! You can compare it with buses that have the same route but go in the opposite direction. If you stand at a bus stop waiting for the bus to go to the nearby town, it does not help you if exactly the same minute the bus leaves the town of your destination and heads the other way. Although it is the same bus, you can not ride it as it goes in the different direction. The straight-line movement of the bus can be characterized by a vector.
To determine whether it is better to use elimination or substitution method to solve a system of equations, first of all, it is advisable to examine closely the coefficients in the equations of the original system.
If the coefficients before one of the variables in two of the equations are the same, but have the opposite sign (or have the same sign - then one of the equations should be simply multiplied by -1) then it would be more practical to use the elimination method. This method is also handy for solving bigger systems that contain three or more variables. ...
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