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Solve the system, please show each step.

x + y + z = -4
-x + 2y + 3z = 3
x - 4y - 2z = -15

2 Answers

3 votes

Answer:

The given equations are

x + y + z = -4


-x + 2 y + 3 z = 3


x - 4 y - 2 z = -15

Writing in matrix form

A= 1 1 1 X= x B= -4

-1 2 3 y 3 ⇒A,X,B are in matrix form.

1 -4 -2 z -15

i.e Ax=B

x =
A^(-1)B

but ,
A^(-1)=Adj.(A)/Determinant A

Determinant of A= 1(-4+12) -1(2-3)+1(4-2)=8+1+2=11

To find Adjoint of matrix A, we will find the cofactor of A and then it's transpose.


a_(11)=-4+12=8,
a_(12)=-[2-3]=1,


,a_(13)=4-2=2,\\,a_(21)=-[-2+4]=-2\\,a_(22)=-2-1=-3,\\a_(23)=-[-4-1]=5,\\a_(31)=[3-2]=1\\,a_(32)=-[3+1]=-4\\,a_(33)=2+1=3

Now taking cofactor, and getting the adjoint

Adjoint (A)= 8 -2 1

1 - 3 -4

2 5 3

Adjoint(A). B= -53

47

-38



(Adjoint (A)* B)/(Determinant A) = -53/11

47/11

-38/11

So, solution set is , x=-53/11, y=47/11, z=-38/11



User FizxMike
by
7.8k points
2 votes

Answer: The solution of the system of equations is
x=(-53)/(11),
y=(47)/(11) and
z=(-38)/(11).

Step-by-step explanation:

The given equations are,


x+y+z=-4 ..... (1)


-x+2y+3z=3 ..... (2)


x-4y-2z=-15 ...... (3)

From equation we get,


x=-4-y-z

Put this value in equation (4) and (5).


-(-4-y-z)+2y+3z=3


3y+4z=-1 .... (4)


(-4-y-z)-4y-2z=-15


-5y-3z=-11 .....(5)

Use elimination method to solve the equations (4) and (5).

Multiply equation (4) by 3 and equation (5) by 4, then add both equations as shown in figure,


-11y=-47


y=(47)/(11)

Put this value in equation (4).


3((47)/(11))+4z=-1


4z=-1-(141)/(11)


4z=(-11-141)/(11)


z=(-152)/(11* 4)


z=(-38)/(11)

Put
y=(47)/(11) and
z=(-38)/(11) in equation (1).


x+(47)/(11)+(-38)/(11)=-4


x+(9)/(11)=-4


x=(-44-9)/(11)


x=(-53)/(11)

Therefore, the The solution of the system of equations is
x=(-53)/(11),
y=(47)/(11) and
z=(-38)/(11).

Solve the system, please show each step. x + y + z = -4 -x + 2y + 3z = 3 x - 4y - 2z-example-1
User FireFighter
by
7.7k points

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