Question

This a question from a test. Its not the exact question but just the short notes I took of it. All help is appreciated. this is a MATRIX ques.
im given: AX=C A=[a c] 4x+2y=7
[b d] 5x-6y=9
the question tells me to find the value of a-b+c+d

Answer 1

this is very hard to see what you are asking

the equations 4x+2y=7, and 5x-6y=9 can be modlled by the matrix equation


Ax=c where A = [4,2;5,-6], x = [x:y] and c=[7;9] giving a-b+c+d = 4-2+5-(-6) = 13

Answer 2

modeled*

Answer 3

err 4-2+5-6 = 1

Answer 4

I hope this is what you are asking

Answer 5

\[A= \left[\begin{matrix}4 & 2 \\5 & -6\end{matrix}\right], X= \left(\begin{matrix}x \\ y\end{matrix}\right), and C = \left(\begin{matrix}7 \\ 9\end{matrix}\right)\]

Answer 6

solve AX=B

Answer 7

they dont want X they want a-b+c+d

Answer 8

thank you both for your help, but im still confused.

Answer 9

the matrix equation Ax = c, where the coefficients are as you listed a,b,c,d
is just another way of representing the system of equations ax+by=c_1, and cx+dy=c_2

here a = 4, b = 2 , c = 5, and d = -6, c_1 = 7 and c_2 = 9

Answer 10

okay, that makes more sence. thank you.

Answer 11

if I give you 2x+3y+5z=5
3x+7y-2z = 4
7x+2y+4y = 1

you would have the equation \(Ax=c\), where

\(A= \left[\begin{matrix}2 & 3 & 5\\3 & 7 & -2 \\7 & 2 & 4\end{matrix}\right], x= \left(\begin{matrix}x \\ y\end{matrix}\right), \text{ and } {c} = \left(\begin{matrix}5 \\ 4 \\ 1\end{matrix}\right)\)