Consider the following two matrices. Why can't the product of the following two matrices be found? A=begin{bmatrix}-1 & 2&3 4 & 0&5 end{bmatrix} text{ and } B=begin{bmatrix}5 & 2 7 & -8 end{bmatrix}

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

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.

y=x^-5

Why solving trigonometry equation for ${\displaystyle x{y}^{\prime }=y\cos \ln \frac{y}{x}}$

Is the following polynomial positive:
$T_k(t)={\left(\frac{t}{2}\right)}^p\sum _{j=0}^k\frac{{(-\frac{t^2}{4})}^j\mathrm{\Gamma }(p+1)}{j!\mathrm{\Gamma }(p+j+1)}.$

Let ${\displaystyle p={\sin 24}^{\circ }}$
1. Then what would ${\displaystyle \cos \left({24}^{\circ }\right)}$ be in terms of p?
2. What would ${\displaystyle \sin \left({168}^{\circ }\right)\cdot \sin (-{78}^{\circ })}$ be in terms of p?

Use cramer's rule to determine the values of $I_1,I_2,I_3$ and $I_4$
$\left[\begin{array}{cccc}13.7& -4.7& -2.2& 0\\ -4.7& 15.4& 0& -8.2\\ -2.2& 0& 25.4& -22\\ 0& -8.2& -22& 31.3\end{array}\right]\left[\begin{array}{c}{I}_1\\ I_2\\ I_3\\ I_4\end{array}\right]=\left[\begin{array}{c}6\\ -6\\ 5\\ -9\end{array}\right]$