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Find the product of the following matrices , if possible
$\left[\begin{array}{cc}6& -9\\ -5& 5\end{array}\right]\left[\begin{array}{c}-1\\ 6\end{array}\right]$
Select the correct choise below and , if necessary , fill in the answer box to complete your choise.
A)$\left[\begin{array}{cc}6& -9\\ -5& 5\end{array}\right]\left[\begin{array}{c}-1\\ 6\end{array}\right]$
B)The product is not defined

Write standart form of complex number ${\displaystyle 5\left({\cos 135}^{\circ }+i{\sin 135}^{\circ }\right)}$

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations.
${\displaystyle y=1-2\sqrt{x}+3}$

Find the sum of the followinf series. Round to the nearest hundredth if necessary.
${\displaystyle 6+12+24+\dots +6144}$
Sum of a finite geometric series:
${\displaystyle S_n=\frac{a_1-a_1{r}^n}{1-r}}$

Prove that if B is symmetric, then $\Vert B\Vert$ is the largest eigenvalue of B.

What transformations of the parent graph of
${\displaystyle f\left(x\right)=\sqrt{x}}$
produce the graphs of the following functions?
a) ${\displaystyle m\left(x\right)=\sqrt{7x-3.5}-10}$
b) ${\displaystyle j\left(x\right)=-2\sqrt{12x}+4}$

Prove that the eigenvalues of a Hermitian matrix are real.

Determine whether the following are polynomials or not: $2x^2+7x+1,1/(x^3+2),6,8x–1,\sqrt{2x+5)}$

$\left[\begin{array}{ccc}0& 2& 4\\ 4& 4& 1\end{array}\right]-\left[\begin{array}{ccc}2& 3& 3\\ -2& 4& -2\end{array}\right]$

Suppose that the dunctions q and r are defined as follows.
${\displaystyle q\left(x\right)=x^2+7}$
$r(x)=\sqrt{x+8}$
Find the following.
${\displaystyle q\cdot r\left(1\right)=?}$
${\displaystyle (r\cdot q)\left(1\right)=?}$

Describe all skew symmetric scalar matrices.

Problem 3. Find the unitary operator $\hat{U}$ which diagonalizes one of the Pauli matrices
${\hat{\sigma }}_x=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$
Obtain the eigenvalues and eigenvectors of ${\hat{\sigma }}_x$

Let D be the set of all students at your school, and let M(s) be a ”s is a math major”, let C(s)”s is a computer science student”, and let E(s) be ”s is an engineering student.” Express each of the following statements using quantifiers, variables, and predicates M(s), C(s) and E(s)

The polynomial ${\displaystyle y=-0.79x^4+3x^3+27.3}$ describes the billions of flu virus particles in a person’s body x days after being infected. Find the number of virus particles, in billions, after 1 day.

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation $\theta$.
$\theta =\{{\tan }^{-1}\frac{5}{12}\}$

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

In the following question there are statements which are TRUE and statements which are FALSE.
Choose all the statements which are FALSE.
1. If the number of equations in a linear system exceeds the number of unknowns, then the system must be inconsistent - thus no solution.
2. If B has a column with zeros, then AB will also have a column with zeros, if this product is defined.
3. If AB + BA is defined, then A and B are square matrices of the same size/dimension/order.
4. Suppose A is an n x n matrix and assume A^2 = O, where O is the zero matrix. Then A = O.
5. If A and B are n x n matrices such that AB = I, then BA = I, where I is the identity matrix.

Describe how to subtract matrices.

Matrix multiplication is pretty tough- so i will cover that in class. In the meantime , compute the following if
$A=\left[\begin{array}{ccc}2& 1& 1\\ -1& -1& 4\end{array}\right],B=\left[\begin{array}{cc}0& 2\\ -4& 1\\ 2& -3\end{array}\right],C=\left[\begin{array}{cc}6& -1\\ 3& 0\\ -2& 5\end{array}\right],D=\left[\begin{array}{ccc}2& -3& 4\\ -3& 1& -2\end{array}\right]$
If the operation is not possible , write NOT POSSIBLE and be able to explain why
a)A+B
b)B+C
c)2A