Question on matrix?

Question

given that c=x-Ax where c and x are 2*1 vectors and A is a 2*2 martix, solve for x by a matrix method, given:
------| 0.2 0.5 |--------- | 50 |
A = | 0.3 0.5 | c= | 90 |

thx first guys!

Answer 1

If I've read your typing of the question correctly, we can say that
x = Ix where I is the 2*2 unit matrix, i.e.

1 0
0 1

Then the righthand side is equal to
(I - A)x, and

I - A = 0.8 -0.5
-0.3 0.5

Left-multiply both sides by the inverse of I - A, i.e. by

2.0 2.0
1.2 3.2
[Rule for inverse of a 2*2 matrix: exchange the elements on the main diagonal (0.8 and 0.5), change the sign on the other two, and divide each element by the determinant. In this case the determinant is
0.8*0.5 - (-0.3)*(-0.5)
= 0.25,
and so dividing by it is to multiply by 4]

If c is 50
90

then this gives

280 = x
348

Answer 2

I assume that you mean matrix
A= [0.2 0.5]
.....[0.3 0.5]
and c=[50]
.......... [90]
now we have c=x-Ax
let x=[a]
.........[b]
then[50]=[a]-[0.2 0.5]*[a]
.......[90]..[b]..[0.3 0.5].[b]
..=[a]-[0.2a+0.5b]
....[b].[0.3a+0.5b]

...= [a-0.2a-0.5b]
........[b-0.3a-0.5b]

[50]=[0.8a-0.5b]
[90]..[0.7a-0.5b]compairing rows
of two sides we get two equations
50=0.8a-0.5
and 90=0.7a-0.5b
solve these for a and b ,u will get matrix x

Answer 3

are you related to steven hawkings ???

Answer 4

.........| 0.2 0.5 |
if A =
.........| 0.3 0.5 |

.......... | 0.8 -0.5 |
I - A =
...........| -0.3 0.5 |

50 = (0.8)x - (0.5) y
90 = (-0.3)x + (0.5) y

x = 280
y = 348