Prove that if A and B are similar n x n matrices, then tr(A) = tr(B).

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.

Find a basis for the space of $2\times 2$ diagonal matrices.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

rocket is launched at an angle of 75 degrees, with a speed of 100 mph. Find the vertical speed of the rocket (vertical component).

I had to solve for x in this equation:
${\displaystyle \sin \left(2x\right)\tan \left(x\right)=\sin \left(2x\right)}$

Let L be an SList. Define a recursive function Wham as follows. B. Suppose L = x. Then Wham$(L)=x\dot{\mid }x.R.$ Suppose L = (X, Y). Then $Wham(L)=Wham(X)+Wham(Y)$. Evaluate Wham (2, 4), (7, 9) , showing all work.

Subtract the polynomials ${\displaystyle (10x^3-5x^2+3x-4)-(6x^3+4x^2-3x-1)}$

How do you simplify ${\displaystyle 5i\cdot i}$?