Solve the following system of equations by matrix method: 5x+3y+z=16,2x+y+3z=19,x+2y+4z=25

Explanation

We have given:`5x+3y+z=16`,
`2x+y+3z=19`,
`x+2y+4z=25`

As we know that the system of linear equation can be written in matrix form as `AX = B`

`implies A=[(5,3,1),(2,1,3),(1,2,4)]`,`X=[(x),(y),(z)]`,`B=[(16),(19),(25)]`

Now find the determinant of `A`,
`|A|= |(5,3,1),(2,1,3),(1,2,4)|`

`|A|=5(4−6)−3(8−3)+1(4-1)`

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