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Please, factor this polynomial: $x^3+1$

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
$A=\left[\begin{array}{cc}-4& 0\\ 1& 3\end{array}\right],B=\left[\begin{array}{cc}-2& 4\\ 0& 1\end{array}\right]$

Cameron stops to get gas soon after beginning a road trip. He checks his distance from home 2 hours after filling his gas tank and checks again 3 hours later. The first time he checked, he was 170 miles from home. The second time, he was 365 miles from home. What equation models Cameron's distance from home as a function of the time since getting gas?

Which transformation does not belong with the other three? Explain your reasoning.

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 A,B and C be square matrices such that AB=AC , If $A\ne 0$ , then B=C.
Is this True or False?Explain the reasosing behind the answer.

In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50, both averaged 12 years of schooling completed, with an SD of 3 years.
a) Predict the educational level of a woman whose husband has completed 18 years of schooling b) Predict the educational level of a man whose wife has completed 15 years of schooling. c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible?

Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B
$A=\left[\begin{array}{cc}4& 1\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}5& 9\\ 0& 7\end{array}\right]$

Show the concept of addition of matrices Along with an example.

If z is a complex number, show that the sum of z and its conjugate is a real number.

State the Properties of matrix addition.

Define Scalar multiplication of matrices?

Find the inverse of the following matrices: $A=\left[\begin{array}{cc}2& 3\\ -1& -4\end{array}\right],B=\left[\begin{array}{ccc}1& -4& 8\\ -3& 5& 7\\ 6& 2& -2\end{array}\right]$

Use long division to rewrite the equation for g in the form
$\text{quotient}+\frac{remainder}{divisor}$
Then use this form of the function's equation and transformations of
${\displaystyle f\left(x\right)=\frac{1}{x}}$
to graph g.
${\displaystyle g\left(x\right)=\frac{3x-7}{x-2}}$

Given the matrices
$A=\left[\begin{array}{cc}5& 3\\ -3& -1\\ -2& -5\end{array}\right]\text{ and }B=\left[\begin{array}{cc}0& -2\\ 1& 3\\ 4& -3\end{array}\right]$
find the 3x2 matrix X that is a solution of the equation. 2X-A=X+B
X=?

compute the indicated matrices $(I_2-D{)}^2$

Write out the system of equations that corresponds to each of the following augmented matrices:
(a)$\left(\begin{array}{cccc}3& 2& |& 8\\ 1& 5& |& 7\end{array}\right)$
(b)$\left(\begin{array}{ccccc}5& -2& 1& |& 3\\ 2& 3& -4& |& 0\end{array}\right)$
(c)$\left(\begin{array}{ccccc}2& 1& 4& |& -1\\ 4& -2& 3& |& 4\\ 5& 2& 6& |& -1\end{array}\right)$
(d)$\left(\begin{array}{cccccc}4& -3& 1& 2& |& 4\\ 3& 1& -5& 6& |& 5\\ 1& 1& 2& 4& |& 8\\ 5& 1& 3& -2& |& 7\end{array}\right)$

Let W be the subspace of all diagonal matrices in $M_{2,2}$. Find a bais for W. Then give the dimension of W.
If you need to enter a matrix as part of your answer , write each row as a vector.For example , write the matrix

Explain the difference between a matrix and a determinant?

For each of the following matrices, determine a basis for each of the subspaces R(AT), N(A), R(A), and N(AT):
$A=\left[\begin{array}{cc}3& 4\\ 6& 8\end{array}\right]$