Use an inverse matrix to solve the equation or system:
{x+2y=15}
{2x+4y=30}

Question

Use an inverse matrix to solve the equation or system:
{x+2y=15}
{2x+4y=30}

anonymous · Answer

Are we unable to find the inverse, or just not sure about any of it?

anonymous · Answer

I'm not sure how to find the inverse

queelius · Answer

First, to get a handle on this, you'll want to rewrite the system of equations into a matrix form.

That is, Ax = b, where A is a 2x2 matrix, x is a vector [x, y], and b is a vector [15, 30]. Do you think you can give me what A is?

queelius · Answer

I should note that x and b are column vectors.

anonymous · Answer

Well, it's not hard for a 2x2 matrix fortunately. If you have a matrix 
$$\left[\begin{matrix}a & b \ c & d\end{matrix}\right]$$ the inverse is:
$$\frac{ 1 }{ ab-bc }*\left[\begin{matrix}d & -b \ -c & a\end{matrix}\right]$$

Do you know how to put the equation given into a matrix equation?

anonymous · Answer

No I don't think so

anonymous · Answer

Well, the numbers that go into your matrix are the coefficients of x and y in each of your equations. So you have:
x + 2y = 15
2x + 4y = 30. So the coefficients of the x's and y's will get plugged into the matrix, giving you:

$$\left[\begin{matrix}1 & 2 \ 2 & 4\end{matrix}\right]$$The question expects you to take this and find its inverse, which can be done using the formula from above.

anonymous · Answer

[4  -2]
[2    1]  ?

anonymous · Answer

$$\left[\begin{matrix}4 & -2 \ -2 & 1\end{matrix}\right]$$So that's part of finding the inverse. I still need to divide that by ad-bc

anonymous · Answer

Once you do ad-bc and try to divide by that quantity, you should notice a big problem :)

anonymous · Answer

Is ad-bc 0?

anonymous · Answer

Yep. And since the formula requires you to divide by ad-bc, you'd be dividing by 0! That's a big no-no. What this tells you is that the matrix DOES NOT have an inverse.

anonymous · Answer

Thank you so much

anonymous · Answer

Well, it still wanted you to get some sort of solution, right? The fact that this matrix doesn't have an inverse gives you two possibilities. I can either have no solution or infinitely many solutions. I think the question would still want you state which one of thse is the case

anonymous · Answer

nice one @Concentrationalizing