solve the system using the cramer's law

Question

4x-3y+z=4 2x+y-3z=8 -x+2yh4z=-4

Answer 1

Assume h should be +.

( 4 -3 1 | 4 )

( 2 1 -3 | 8 )

(-1 2 4 | -4 )
 

The above matrix is a numerical representation of the problem to be solved using Cramer's Rule.

First, we calculate the determinant to the left of the vertical stroke:

4(4+6)+3(8-3)+1(4+1)=40+15+5=60.

Next we substitute the figures in the column to the right of the vertical stroke in turn for the figures in the 3 columns (representing x, y and z), and calculate the determinants for each:

x: 4(4+6)+3(32-12)+1(16+4)=40+60+20=120; x=120/60=2.

y: 4(32-12)-4(8-3)+1(-8+8)=80-20+0=60; y=60/60=1.

z: 4(-4-16)+3(-8+8)+4(4+1)=-80+0+20=-60; z=-60/60=-1.