Use a system of linear equations to find the quadratic function f(x) = ax^22+bx+c that satisfies the given conditions. Solve the system using matrices. f(-2) = 6, f(1) = -3, f(2) = -14 f(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 and B are nn matrices, then $(A-B{)}^2=A^2-2AB+B^2$

Use the definition of the matrix exponential to compute eA for each of the following matrices:
$A=\left[\begin{array}{ccc}1& 0& -1\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

Find if possible the matrices:
a) AB b) BA.
$A=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right],B=\left[\begin{array}{cc}0& 0\\ 5& -6\end{array}\right]$

Use the given coding matrices to encode and then decode the given message HELP.
$A=\left[\begin{array}{cc}4& -1\\ -3& 1\end{array}\right]$ and its inverse $A^{-1}=\left[\begin{array}{cc}1& 1\\ 3& 4\end{array}\right]$

Find the quadratic function that is the best fit for​ f(x) defined by the table below x f(x) 0 1 2 -0.6 4 -1.4 6 -1.4