Find All Values of x

David Cohen

NOTE: Look for additional David Cohen in my Precalculus FB private group.

Here's a matrix algebra problem.

 

first find determinant



in this case determinant is

1*1*0-1*1*5-x*1*0+x*1*4+x^2*1*5-x^2*1*4=0-5-0+4x+5x^2-4x^2=-5+4x+x^2


set x^2+4x-5=0 solve for x

x^2-x+5x-5=0
(x^2-x)+(5x-5)=0
x(x-1)+5(x-1)=0
(x+5)(x-1)=0
solutions: x=1, x=5

 

Not as bad as I thought. I don't recall Matrix Algebra in the Ron Larson textbook. If it is there, we will go through it together.

 

The way I would do this determinant:
\(\left|\begin{array}{ccc}1 & x & x^2 \\ 1 & 1 & 1 \\ 4 & 5 & 0\end{array}\right|\)

expand on the right co

 

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