What is the determinant of the coefficient matrix of the system {4x+3y+2z=0 -3x+y+5z=0 -x-4y+3z=0

  130

Step-by-step explanation:

You want the determinant of the matrix ...

One way to figure it is as the difference between the sum of products of the down-diagonals and the sum of products of the up-diagonals:

  D = (4)(1)(3) +(3)(5)(-1) +(2)(-3)(-4) -(-1)(1)(2) -(-4)(5)(4) -(3)(-3)(3)

  = 12 -15 +24 +2 +80 +27

  D = 130

The determinant of the coefficient matrix is 130.

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Many scientific and graphing calculators and web sites can perform this calculation for you.

24+x=y

step-by-step explanation:

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0