Question

@Hero

Answer 1

@TQKMB go ahead and post your first question.

Answer 2

Okay, so for this question, notice that you have a matrix of the form
\(Ax = B\) where \(A\) and \(B\) are given matrices. And the goal here is to isolate x. Do you agree?

Answer 3

Sure

Answer 4

And to isolate x, we need to apply the inverse of A on both sides correct?

Answer 5

OK

Answer 6

And when we do that, we will have \(x = A^{-1}B\). Notice that in order to get the proper value of x, it must be multiplied in that order. If no one hasn't told you yet, \(A^{-1}(B) \ne BA^{-1}\)

Answer 7

In other words, for matrices, the associative property does not apply.

Answer 8

OK

Answer 9

By the way, as you know

\(A = \begin{bmatrix} 9 & 4 \\ 2 & 1 \end{bmatrix}\)

We need to find \(A^{-1}\). Do you remember the formula for how to find \(A^{-1}\)?

Answer 10

I don't know if we learned that yet. If we have I probably forgot it.

Answer 11

So in general,

\(A^{-1} = \dfrac{1}{|A|}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\)

Answer 12

Have you seen that before?

Answer 13

NO

Answer 14

What have you been learning about in class? Augmented matrix?

Answer 15

Well, anyway, that's the formula for the inverse of a matrix. By the way, |A| is the notation for the determinant of a matrix. And for a \(2 \times 2\) matrix, \(|A| = ad - bc\)

Answer 16

OK

Answer 17

So ultimately,

\(A^{-1} = \dfrac{1}{ad - bc}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\)

Answer 18

OK

Answer 19

In other words, o find \(A^{-1}\) all you have to do is just plug in the corresponding values for a, b, c, d from your given matrix \(A\) into the formula for \(A^{-1}\) and simplify.

Answer 20

OK

Answer 21

Go ahead. Try that and let me know what you get.

Answer 22

How do I solve that.

Answer 23

I just told you what to do. Plug the values of matrix A in to the formula for \(A^{-1}\).

Remember,

\(A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} 9 & 4 \\ 2 & 1 \end{bmatrix} \)

Answer 24

The formula for \(A^{-1}\) is posted above.

Answer 25

So what do I do after that? @Hero

Answer 26

Have you plugged in the given values for \(A\) in to the formula for \(A^{-1}\). After calculation you should end up with the appropriate matrix.

Answer 27

So whats the answer.

Answer 28

I don't understand anything your saying. I don't understand the steps.