x – y + 2z = 132x + xy – z = -6-x + 3y + z = -7?

Question

a. Provide a coefficient matrix corresponding to the system of linear equations.

b. What is the inverse of this matrix?

c. What is the transpose of this matrix?

d. Find the determinant for this matrix.

Answer 1

x - y + 2z = 132
x + xy - z = - 6<--------looks dodgy!
-x + 3y + z = - 7

Answer 2

Ok go

1) There is an "ERROR" in the 2nd equation

2) Check

http://es.answers.yahoo.com/question/index;_ylt=Atp74MEWKhyiPpiLngSF50lo.gt.;_ylv=3?qid=20071228115325AAjZfTQ&show=7#profile-info-T4YqS7PXaa

For that reason , i am assuming " 2x + 2y – z = 6 "

Then, the system of linear equations "CORRECT" is

..x .– y + 2z = 13
2x + 2y – z = 6
-x + 3y + z = -7
------------------------

------Coefficients-------

│.1.....-1.....2....│.x = ¦...13 ¦
│.2......2....-1....│.y = ¦.....6 ¦
│-1......3.....1....│.z = ¦....-7 ¦


Now

│.1.....-1.....2....│.
│.2......2....-1....│=D
│-1......3.....1....│

D= 22
--------------¦


For "X"

│13....-1.....2....│.
│.6......2....-1....│
│-7......3.....1....│
-----------------------...= D(X)
..........D

X= 128 / 22.......> X= 5,82
--------------------------------------...


For "Y"

│.1.....13.....2....│.
│.2.......6....-1....│
│-1......-7.....1....│
------------------------...= D(Y)
..........D

Y= -30 / 22 =......> Y= -1,36
--------------------------------------...


For "Z"

│.1.....-1...13....│.
│.2......2.....6....│
│-1......3....-7....│
-----------------------...= D(Z)
..........D

Z= 64 / 22......> Z= 2,91
------------------------------------¦


Los coefficent are: X = 5,82; Y = -1,36; Z= 2,91
______________________________________...

---------Inverse--------

¦ .1...-1....2 ¦
¦ .2....2...-1 ¦ = A
¦ -1....3....1 ¦


¦ .1...-1....2 ¦
¦ .2....2...-1 ¦ => D(A) = 22
¦ -1....3....1 ¦


¦ .2...-1 ¦
¦ .3....1 ¦....¦ a11 ¦= 5

¦ .2...-1 ¦
¦ -1....1 ¦....-¦ a12 ¦ = -1

¦ .2....2 ¦
¦ -1....3 ¦....¦ a13 ¦= 8

¦ -1....2 ¦
¦ .3....1 ¦....-¦ a21¦ = 7

¦ .1....2 ¦
¦ -1....1 ¦....¦ a22 ¦= 3

¦ .1...-1 ¦
¦ -1....3 ¦....-¦ a23 ¦ = -2

¦ -1.....2 ¦
¦ .2....-1 ¦....¦ a31 ¦= -3

¦ .1.....2 ¦
¦ .2....-1 ¦....-¦ a32 ¦ = 5

¦ 1....-1 ¦
¦ 2.....2 ¦....¦ a33 ¦= 4


Now A^-1


.........¦..5.....7....-3 ¦
.1/22..¦.-1.....3.....5 ¦
.........¦..8....-2.....4 ¦

______________________________________...

----transpose----

¦ .1...-1....2 ¦
¦ .2....2...-1 ¦ = A
¦ -1....3....1 ¦


Now A^T

¦ .1....2...-1 ¦
¦ -1....2....3 ¦ = T
¦ .2...-1....1 ¦

______________________________________...

-----Determinat------

│.1.....-1.....2....│= (1x2x1)+(2x3x2)+(-1x-1-1)=2+12-1= 13
│.2......2....-1....│= -(2x2x-1)-(-1x3x1)-(1x-1x2)= 4+3+2=9
│-1......3.....1....│= 13 +9 =22

D = 22
-----------¦


Bye.Bye

Answer 3

1….X-Y+2Z = 132
2….X+XY-Z = -6
3….-X+3Y+Z = -7 (-2 times firstly, -1 times secondly)

Firstly (from 1&3 equation)
X-Y+2Z = 132
2X-6Y-2Z = 14

3X-7Y = 146 and 3X-4Y = 146+3Y ( equation 4)
and X = (146+7Y)/3…………(equation 5)

Secondly (from 1&2&3 equation)
X-Y+2Z = 132
X+XY-Z = -6
X-3Y-Z = -7

3X-4Y+XY = 133 (equation 6)

from equation 4&6
146+3Y+XY = 133 and 3Y+XY = -13….. (equation 7)

from equation 5&7
7Y^2+155Y+39 = 0
from Deltha = b^2-4ac and Y= - b ± Delta^0,5/2a
Y = -0,25454
X = 48,0725
Z = 41,83648

Answer 4

The second equation seems to be nonlinear with the presence of xy term.