Question

What is the solution of the matrix equation?

Answer 1

Ax=b, if it has a solution, can be determined by the augment: (A|b) to (I|x)

Answer 2

do you know how to invert a matrix?$$A=\begin{bmatrix}9&4\\2&1\end{bmatrix}\\A^{-1}=\frac1{\det A}\begin{bmatrix}1&-4\\-2&9\end{bmatrix}=\frac1{9(1)-4(2)}\begin{bmatrix}1&-4\\-2&9\end{bmatrix}=\begin{bmatrix}1&-4\\-2&9\end{bmatrix}$$

Answer 3

so$$Ax=\begin{bmatrix}9&-6\\-1&-8\end{bmatrix}\\A^{-1}Ax=\begin{bmatrix}1&-4\\-2&9\end{bmatrix}\begin{bmatrix}9&-6\\-1&-8\end{bmatrix}\\x=\begin{bmatrix}1&-4\\-2&9\end{bmatrix}\begin{bmatrix}9&-6\\-1&-8\end{bmatrix}$$

Answer 4

multiplying we get:$$x=\begin{bmatrix}1&-4\\-2&9\end{bmatrix}\begin{bmatrix}9&-6\\-1&-8\end{bmatrix}=\begin{bmatrix}1(9)+-4(-1)&1(-6)+-4(-8)\\-2(9)+9(-1)&-2(-6)+9(-8)\end{bmatrix}=\begin{bmatrix}13&26\\-27&-60\end{bmatrix}$$

Answer 5

..so what the next step?

Answer 6

do i multiply that all as a whole to get 13, -27 etc?

Answer 7

@oldrin.bataku

Answer 8

@Buddhayourlord&savoir that matrix at the end is the product evaluated

Answer 9

Are you insisting thats the answer?
I have multiple choice and none of this matches :/

Answer 10

;-;
@amistre64 can you please lead me through this?

Answer 11

:(

Answer 12

http://www.wolframalpha.com/input/?i=linearsolve%5B%5B%5B9%2C4%5D%2C%5B2%2C1%5D%5D%2C%5B%5B9%2C-6%5D%2C%5B-1%2C-8%5D%5D%5D

Answer 13

this agrees with my solution

Answer 14

:/

Answer 15

http://www.wolframalpha.com/input/?i=rref%7B%7B9%2C4%2C-9%2C-6%7D%2C%7B2%2C1%2C-1%2C-8%7D%7D