Use the inverse matrix mathod to solve the following system of liear equations.
a. 2x+3y+z= -1
3x+3y+z= 1
2x+4y+z= -2
b. 2x+3y+z= 4
3x+3y+z= 8
2x+4y+z= 5
c. 2x+3y+z= 2
3x+3y+z= -1
2x+4y+z= 4
2006-08-17 15:33:03 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
come on
who is going to try to type a bunch of matrix algebra
here is a start
2 3 1 -1
3 3 1 1
2 4 1 -2
there is your matrix, now you have to use algebraic type maneuvers to get a matrix that looks like
1 0 0 x
0 1 0 y
0 0 1 z
divide the top line of original matrix by 2 and you get a new top line:
1 3/2 1/2 -1/2
see, you have the one you need, now you need some zeros
you have to multiply the next line in the original matrix by something that will allow you to add and get zero
read your book
use your calculator
get a tutor
something
Y!answers is no place for matrix algebra
2006-08-17 15:44:39 · answer #1 · answered by enginerd 6 · 0⤊ 0⤋
Basically, let Ax=B where A, x, B are matrixes. If we can find the inverse of matrix A, let's call it C, we can see that CAx=CB. CA = I, the identity matrix. So here goes:
(a) x = 2, y = -1, z = -2
(b) x = 4, y = 1, z = -7
(c) x = -3, y = 2, z = 2
Just for additional information, to find the inverse of a matrix, put your matrix in the form [ I | A ]. Perform some row operations until this becomes [ C | I ]. C would be the inverse of A.
2006-08-17 22:51:45 · answer #2 · answered by khensthoth4ever 2 · 0⤊ 0⤋
The equations are all in the form
2x + 3y + z = a
3x + 3y + z = b
2x + 4y + z = c
Let us solve:
Subtract the first equation from the 2nd equation
x = b - a
Subtract the first equation from the 3rd equation
y = c - a
Substitute these values to any equation and get
z = 6a - 2b - 3c
For the 1st triple,
a = -1 b = 1 c = -2
etc.
^_^
2006-08-18 08:47:55 · answer #3 · answered by kevin! 5 · 0⤊ 0⤋
Just on (a).
(sorry for the mess, couldn't figure out how to align them properly)
/2 3 1\/x\/-1\
|3 3 1||y|=| 1|
\2 4 1/\z/\-2/
/-2 -3 -1 \ /x\/1\
| 3 3 1 ||y |=|1 |
\-1 -2 -0.5/ \z/\1/
/x\/-2 -3 -1 \-1/1\
|y|=| 3 3 1 ||1 |
\z/\-1 -2 -0.5/\1/
Thsu, x, y, and z equal to the sums of the 1st, 2nd, and 3rd row of the inverse of the 3x3 matrix.
2006-08-17 22:49:46 · answer #4 · answered by back2nature 4 · 0⤊ 0⤋
For this type of question you may send your e- mail address I will solve them and send it back
2006-08-18 00:51:42 · answer #5 · answered by Amar Soni 7 · 0⤊ 0⤋
go to hotmath.com and find ur math book
2006-08-17 23:00:28 · answer #6 · answered by Anonymous · 0⤊ 0⤋
WTF how do you do that. That's impossible, I tells ya!
2006-08-17 22:40:02 · answer #7 · answered by Anonymous · 0⤊ 0⤋
wtf
2006-08-17 23:22:12 · answer #8 · answered by Navdeep B 3 · 0⤊ 0⤋