Linear Algebra

Let A be a 2 x 2 matrix with A^3 = O. Prove that A^2 = O. Where O is the zero matrix. (Note: I've said nothing about the invertibility of A, it may or may not be invertible).

Algebraic equations

As provided by E. Galua theory the general algebraic equations for a polynomial of fourth order ax^4 + bx^3 + cx^2 + dx + f=0 (*) is the maximum order type of algebraic equations the solution to which one can write down in radical expressions. Among all the equations of fourth ...continues

Equalities

Clarification on equalities. Please see attached file.

Clarification on an answer

Understanding steps in a formula - There are certain points I do not understand in the answer an OTA gave me to a question I had asked yesterday, and I attach a document which sets out the original question and the points in the reasoning where I am having trouble.

Comparing Areas

Calculate AREA of Shape 1 then calculate the area of Re-arranged Shape 1. Did you get the same result? Why are they different? Please see the attached document.

Linear equation with 3 variables

1. 6x - y + 5z =47 2. -6x + 9y +4z = 10 3. -7x -6y + z = -91 I have tried to work this out several ways and cant seem to get very far. So far I have taken row 1 and added it to row 2 which left me with 8y + 9z =57 and then I took row 1 and multiplied it by 7 and row 3 and multiplied it by 6 and added those together and c ...continues

Equation help

solve for p where a=p(1+r)^t Please explain steps. My first step is: a/p=(1+r)^t but I don't know how to move the "a"

algebra equation help

solve for r where s=rl-a/r-1 Please show steps to solution.

equation help

solve for n where l=a+(n-1)d Please show steps

equation help

solve for a where s=n/2(2a+(n-1)d) Please show steps to solution