Question

Can someone help me with matrices?

Answer 1

Need help solving the equation

Answer 2

@mollyhatesmath

Answer 3

@perl

Answer 4

Given \(Ax=B\), multiplying both sides by the inverse of \(A\) will isolate \(x\).

If \(A=\begin{bmatrix}2&1\\4&3\end{bmatrix}\), then the inverse is
\[A^{-1}=\frac{1}{\begin{vmatrix}2&1\\4&3\end{vmatrix}}\begin{bmatrix}-3&4\\1&-2\end{bmatrix}=\frac{1}{2}\begin{bmatrix}-3&4\\1&-2\end{bmatrix}\]
Since \(A^{-1}A=I\), you have
\[\begin{bmatrix}x\\y\end{bmatrix}=\frac{1}{2}\begin{bmatrix}-3&4\\1&-2\end{bmatrix}\begin{bmatrix}10\\-2\end{bmatrix}=\cdots\]

Answer 5

I am still confused. Could you explain how you got the answer? @SithsAndGiggles

Answer 6

Let's make sure we're on the same page. Do you know what a determinant is? How to calculate it for a 2x2 matrix?

Do you know what an inverse matrix is? How to calculate it?

Answer 7

yes

Answer 8

another approach is to use an augmented matrix, but its just method over madness.

Answer 9

another way is to just create the system, ad solve the old algebraic way ..

2x + 1y = 10
4x + 3y = -2

how do we solve the system?

Answer 10

Thanks! I got x=11 and y=-12

Answer 11

@amistre64

Answer 12

2x + 1y = 10
4x + 3y = -2


-6x - 3y = -30
4x + 3y = - 2
--------------
-2x = -32

im not getting x = 11