# Vectors

#### sami123

##### New member
2. If p = 3i - j, q = 4i + 5j and r = -6i + 2j
a. can you find the find numbers s and t such that q = sp + tr
Can u any one tell me when it is not possible to find numbers like s and t?

#### pka

##### Elite Member
2. If p = 3i - j, q = 4i + 5j and r = -6i + 2j
a. can you find the find numbers s and t such that q = sp + tr
Can u any one tell me when it is not possible to find numbers like s and t?
You want to solve: $$\displaystyle s<3,-1>+t<-6,2>=<4,5>$$
You should have a system of two equations in two unknowns.

#### tkhunny

##### Moderator
Staff member
Have you considered writing out the addition and seeing if it leads to a rational system that is readily solved?

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#### sami123

##### New member

You want to solve: $$\displaystyle s<3,-1>+t<-6,2>=<4,5>$$
You should have a system of two equations in two unknowns.
You want to solve: $$\displaystyle s<3,-1>+t<-6,2>=<4,5>$$
You should have a system of two equations in two unknowns.
The answer given in book is not exist
I still not understand what is the condition when we are not able to find numbers??

#### tkhunny

##### Moderator
Staff member
Did you get the system that must be solved?

You could also notice that r = -2p. That could lead to interesting conclusions.

You can't have NO idea,

#### pka

##### Elite Member
You want to solve: $$\displaystyle s<3,-1>+t<-6,2>=<4,5>$$
You should have a system of two equations in two unknowns.
The answer given in book is not exist
I still not understand what is the condition when we are not able to find numbers??
The book is correct. But it was you task to discover that fact for yourself. It is not ours.
$$\displaystyle \left\{ \begin{array}{l}3s - 6t = 4\\ - s + 2t = 5\end{array} \right.$$
It is easy to see that system has no solution. Again that was your job.