Evaluate each determinant.

$$\left| \begin{array} { c c } { - 5 } & { - 1 } \\ { - 2 } & { - 7 } \end{array} \right|$$

In the following exercise, find a formula for the inverse function. Assume these functions are defined on domains on which they are invertible.

$$l(x)=\sqrt{1-2 x^2}$$

Evaluate the determinant of the given matrix by cofactor expansion.

$$\left(\begin{array}{rrrrr}{2} & {2} & {0} & {0} & {-2} \\ {1} & {1} & {6} & {0} & {5} \\ {1} & {0} & {2} & {-1} & {-1} \\ {2} & {0} & {1} & {-2} & {3} \\ {0} & {1} & {0} & {0} & {1}\end{array}\right)$$

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Evaluate the determinant of the given matrix.

$$A = \left[ \begin{array} { r r r r r } { 0 } & { 0 } & { 0 } & { 8 } & { 4 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 1 } \\ { 0 } & { 0 } & { 2 } & { 0 } & { 0 } \\ { 2 } & { - 3 } & { 0 } & { 0 } & { 0 } \\ { 4 } & { - 2 } & { 0 } & { 0 } & { 0 } \end{array} \right].$$

For the following exercises, use the determinant function on a graphing utility.

$$\left|\begin{array}{llll} 1 & 0 & 0 & 0 \\ 2 & 3 & 0 & 0 \\ 4 & 5 & 6 & 0 \\ 7 & 8 & 9 & 0 \end{array}\right|$$

Solve the problem given in rectangular coordinates by converting it to polar coordinates. $\nabla^{2} u(x, y)=0 \text { for } x^{2}+y^{2}<25, u(x, y)=x y \text { for } x^{2}+y^{2}=25$

Circle the you in each sentence. Then write a third-person pronoun to complete the sentence correctly.

The lions crept along in the high grass, which is what you do in stalking prey.

The symbol [x] means the greatest integer less than or equal to x (for example, [3] = 3, [2.1] = 2, [−4.5] = −5). Expand $x-[x]-\frac{1}{2}$ in an exponential Fourier series of period 1. Hint: Sketch the function.

Is the matrix Hermitian? SkewHermitian? Unitary? Find their eigenvalues and eigenvectors.

$$\left[\begin{array}{lll}0 & 0 & i \\ 0 & i & 0 \\ i & 0 & 0\end{array}\right]$$

Find a basis of eigenvectors that form a unitary system. (Show the details.)

$$\left[\begin{array}{cc}0 & 3 i \\ -3 i & 0\end{array}\right]$$

Describe how a cnidarian captures and ingests its prey.

Replace the symbol $\square$ with either $=$ or $\neq$ to make the resulting statement true for all real numbers $a, b$, $c$, and $d$, whenever the expressions are defined.

$$(a \div b) \div c ~\square ~ a \div(b \div c)$$

Find the determinant of each matrix.

$$\left[\begin{array}{rrr}2 & 3 & 5 \\ -1 & 4 & 4 \\ 5 & 0 & 9\end{array}\right]$$

By considering the graph, identify all points of discontinuity.

$$f(x)=\tan x$$