Matrix Algebra Prove

[nycmathguy]

David Cohen

Enjoy. For all my math friends.

 

[MathLover1]

again, use determinant

in this case determinant is:

1(1+x)(1+x^2) -1*1*1 -1*1(1+x) +1*1*1+1*1*1-1*(1+x)*1
=(1+x)(1+x^2) -1 -(1+x^2) +1+1-(1+x)
=(1+x)(1+x^2) -(1+x^2) +1-(1+x)
=(1+x)(1+x^2) -1-x^2 +1-1-x............multiply (1+x)(1+x^2)
=x^3+x^2+x+1-1-x^2 +1-1-x.......simplify, cancel
=x^3

 

[nycmathguy]

again, use determinant

View attachment 1074

in this case determinant is:

1(1+x)(1+x^2) -1*1*1 -1*1(1+x) +1*1*1+1*1*1-1*(1+x)*1
=(1+x)(1+x^2) -1 -(1+x^2) +1+1-(1+x)
=(1+x)(1+x^2) -(1+x^2) +1-(1+x)
=(1+x)(1+x^2) -1-x^2 +1-1-x............multiply (1+x)(1+x^2)
=x^3+x^2+x+1-1-x^2 +1-1-x.......simplify, cancel
=x^3

The main thing is using the formula listed above. Hopefully there is a chapter on Matrix Algebra in the Ron Larson textbook. If not, I can always use the David Cohen textbook for this topic

 

[MathLover1]

there must be a chapter on Matrix Algebra in the Ron Larson textbook

 

[nycmathguy]

there must be a chapter on Matrix Algebra in the Ron Larson textbook

If you are right, Matrix Algebra is still many chapters away. If not, we can use the David Cohen textbook. By the way, do you know Linear Algebra? I may want to learn the essentials of this course in the future.

 

[MathLover1]

let's do precalculus first

 

[nycmathguy]

let's do precalculus first

Yes, of course. We will complete precalculus first and then step into calculus l, ll, and lll. Matrix algebra is part of linear algebra but David Cohen has a chapter on the basics of matrix algebra. I will post matrix algebra basics later on in our journey.

At the rate I'm going, I should be in calculus 1 hopefully by March 2022. I am only posting the essentials of precalculus. I just don't have time to learn everything. You are retired. I am not even near retirement. I may need to work up to 70 years old to get a somewhat decent social security.

More math later on. Trying to get some extra sleep.