Solve the system of linear equations using matrices.3x-2y-4=02y=12-x

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.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

If A is diagonalizable and for all eigenvalues , $\lambda \text{ of }A,|\lambda |=1$ , then A is unitary. True or False?

The function f is defined, for ${\displaystyle x\ge 0}$ , by ${\displaystyle f\left(x\right)=4-3\cos \left(\frac{x}{2}\right)}$
Given that ${\displaystyle f(na+b)=2.5}$ where a is positive constant and n=0,1,2,..., find the smallest possible value of b and least value of a.

Solve the equation:
${\displaystyle (2x-5)+(3x^2+7x+10)}$

Finding $\cot (\frac{\pi }{12})$
Given:
$\cot (\theta -\varphi )=\frac{\cot \theta \cot \varphi +1}{\cot \theta -\cot \varphi }$
And:
$\cot \frac{\pi }{3}=\frac{1}{\sqrt{3}};\cot \frac{\pi }{4}=1$
$\frac{\frac{1}{\sqrt{3}}(1)+1}{\frac{1}{\sqrt{3}}-1}$
$\frac{1+\sqrt{3}}{1-\sqrt{3}}$

How do you find the power ${\displaystyle [3{(\cos \left(\frac{\pi }{6}\right)+i\sin \left(\frac{\pi }{6}\right)]}^3}$ and express the result in rectangular form?