SOLUTION: using cramers rule solve the following systems of linear equations a. x-2y+3z = -7 2y = 6 2x-z = 5 b. 3x - y + 2z = 13 -x + 4y + 2z= -1 4y

Algebra ->  Finance -> SOLUTION: using cramers rule solve the following systems of linear equations a. x-2y+3z = -7 2y = 6 2x-z = 5 b. 3x - y + 2z = 13 -x + 4y + 2z= -1 4y      Log On


   

Question 1123039: using cramers rule solve the following systems of linear equations
a. x-2y+3z = -7
2y = 6
2x-z = 5
b. 3x - y + 2z = 13
-x + 4y + 2z= -1
4y + 3z = 4
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a.
x-2y%2B3z+=+-7
2y+=+6
2x-z+=+5
Your matrix:


Write down the main matrix and find its determinant:
matrix%283%2C3%2C1%2C%09-2%2C%093%2C%09%0D%0A0%2C%092%2C%090%2C%09%0D%0A2%2C%090%2C%09-1%29
Δ = -14

Replace the 1st column of the main matrix with the solution vector and find its determinant:

matrix%283%2C3%2C+-7%09%2C-2%09%2C3%2C%0D%0A6%09%2C2%09%2C0%2C%0D%0A5%09%2C0%09%2C-1%29

Δ1+=+-28
Replace the 2nd column of the main matrix with the solution vector and find its determinant:

matrix%283%2C3%2C1%09%2C-7%2C%093%2C%0D%0A0%09%2C6%09%2C0%2C%0D%0A2%09%2C5%09%2C-1%29

Δ2+=+-42


Replace the 3rd column of the main matrix with the solution vector and find its determinant:
matrix%283%2C3%2C%0D%0A1%09%2C-2%2C%09-7%2C%0D%0A0%09%2C2%09%2C6%2C%0D%0A2%2C%090%09%2C5%29

Δ3+=+14

x%5B1%5D = Δ1 /Δ =+%28-28%29+%2F+%28-14%29+=+2
x%5B2%5D = Δ2 /Δ = %28-42%29+%2F+%28-14%29+=+3
x%5B3%5D = Δ3/Δ =+14+%2F+%28-14%29+=+-1

Solution set:
x%5B1%5D+=+2
x%5B2%5D+=+3
x%5B3%5D=+-1


b.
3x+-+y+%2B+2z+=+13
+-x+%2B+4y+%2B+2z=+-1
+4y+%2B+3z+++=+4

Your matrix


Write down the main matrix and find its determinant:


matrix%283%2C3%2C%0D%0A3%09%2C-1%09%2C2%2C%0D%0A-1%09%2C4%09%2C2%2C%0D%0A0%09%2C4%09%2C3%29

Δ = 1

Replace the 1st column of the main matrix with the solution vector and find its determinant:

matrix%283%2C3%2C13%09%2C-1%09%2C2%2C%0D%0A-1%2C%094%09%2C2%2C%0D%0A4%09%2C4%09%2C3%29

Δ1+=+1

Replace the 2nd column of the main matrix with the solution vector and find its determinant:

matrix%283%2C3%2C3%2C%0913%09%2C2%2C%0D%0A-1%09%2C-1%09%2C2%2C%0D%0A0%09%2C4%09%2C3%29
Δ2+=+-2

Replace the 3rd column of the main matrix with the solution vector and find its determinant:

matrix%283%2C3%2C3%09%2C-1%09%2C13%2C%0D%0A-1%09%2C4%09%2C-1%2C%0D%0A0%09%2C4%09%2C4%29

Δ3+=+4


x%5B1%5D = Δ1 / Δ = 1+%2F+1+=+1
x%5B2%5D = Δ2 / Δ =+%28-2%29+%2F+1+=+-2
x%5B3%5D+= Δ3 / Δ =+4+%2F+1+=+4


Solution set:
x%5B1%5D+=+1
x%5B2%5D+=+-2
x%5B3%5D+=+4