simplify the following matrix expression: begin{bmatrix}1 & 5 2 & -3-3&7 end{bmatrix}-2begin{bmatrix}2 & -3 8 & 5-1&-1 end{bmatrix}=?

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

Calculate the derivative of the following function
${\displaystyle f\left(x\right)-\ln \frac{(2x-1){(x+2)}^3}{{(1-4x)}^2}}$

If $3\left[\begin{array}{cc}{x}_1& x_2\\ x_3& x_4\end{array}\right]=\left[\begin{array}{cc}{x}_1& 2\\ -1& 4x_4\end{array}\right]+\left[\begin{array}{cc}4& x_1+x_2\\ x_3+x_4& 3\end{array}\right]$
1. $x_1=-2,x_2=2,x_3=-2,x_4=-3$
2. $x_1=2,x_2=-2,x_3=-2,x_4=-3$
3. $x_1=2,x_2=2,x_3=2,x_4=-3$
4. $x_1=2,x_2=2,x_3=-2,x_4=3$
5, $x_1=2,x_2=2,x_3=-2,x_4=-3$

For each topic, decide how a scatterplot of the data would likely look. Explain your reasoning. Speed of a runner and amount of time to complete a race

Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) Addition of matrices is not commutative.
(b) The transpose of the sum of matrices is equal to the sum of the transposes of the matrices.