How do you solve 3y−z=−1, x+5y−z=−4, −3x+6y+2z=11 using matrices?

1 Answer
Alan P.
Feb 21, 2016

Use Cramer's Rule (with Determinants) to get
XXX(x,y,z)=(−3,0,1)

Explanation:

Using the coefficient of x,y,andz plus the equated constants as columns we can write these equations in matrix form.

If D is the determinant of the variable coefficient matrix
and Da,a∈{x,y,z} is the determinant of the variable coefficient matrix with the column for variable a replaced by the equated constants column,

Cramer's Rule tells us that:
XXXa=DaD for a∈{x,y,z}

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An interesting point to observe, because of the way computers perform (what is called "floating point") arithmetic the value of Dy shows up as being
XXX3E−16=0.0000000000000003 instead of 0
which, in turn, cause y to display as
XXX−1.9E−17=−0.000000000000000019 instead of 0

You must be prepared to apply reasonable interpretations when working with computer generated outputs.

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