User:InvaderJim42/Sandbox1

A


H(1) = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} $$

$$ H(1) = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} $$

B


H(k) = \begin{bmatrix} H(k-1) & H(k-1)\\ H(k-1) & -H(k-1)\end{bmatrix} $$

$$ H(k) = \begin{bmatrix} H(k-1) & H(k-1)\\ H(k-1) & -H(k-1)\end{bmatrix} $$

C

 * $$\frac{1}{2}Q\left[f(a) + 2f(a+Q) + 2f(a+2Q) + 2f(a+3Q)+\dots+f(b)\right]$$

$$ \frac{1}{2}Q\left[f(a) + 2f(a+Q) + 2f(a+2Q) + 2f(a+3Q)+\dots+f(b)\right] $$

D

 * $$\left \vert \int_{a}^{b} f(x) - A_{trap} \right \vert \le \frac{M_2(b-a)^3}{(12n^2)}$$

$$ \left \vert \int_{a}^{b} f(x) - A_{trap} \right \vert \le \frac{M_2(b-a)^3}{(12n^2)} $$

E

 * $$\sum_{x_i\in P} f(c_i)(g(x_{i+1})-g(x_i))$$

$$\sum_{x_i\in P} f(c_i)(g(x_{i+1})-g(x_i))$$

F

 * $$\int_a^b f(x) \, dg(x)=f(b)g(b)-f(a)g(a)-\int_a^b g(x) \, df(x)$$

$$\int_a^b f(x) \, dg(x)=f(b)g(b)-f(a)g(a)-\int_a^b g(x) \, df(x)$$

G


\begin{bmatrix} 1 & 0 & 2 \\   -1 & 3 & 1 \\  \end{bmatrix} \times \begin{bmatrix} 3 & 1 \\   2 & 1 \\    1 & 0  \end{bmatrix} = \begin{bmatrix} (1 \times 3 +  0 \times 2  +  2 \times 1) & (1 \times 1   +   0 \times 1   +   2 \times 0) \\ (-1 \times 3 +  3 \times 2  +  1 \times 1) & (-1 \times 1   +   3 \times 1   +   1 \times 0) \\ \end{bmatrix} = \begin{bmatrix} 5 & 1 \\   4 & 2 \\  \end{bmatrix} $$

$$   \begin{bmatrix} 1 & 0 & 2 \\    -1 & 3 & 1 \\   \end{bmatrix} \times \begin{bmatrix} 3 & 1 \\    2 & 1 \\     1 & 0   \end{bmatrix} =  \begin{bmatrix} (1 \times 3 +  0 \times 2  +  2 \times 1) & (1 \times 1   +   0 \times 1   +   2 \times 0) \\ (-1 \times 3 +  3 \times 2  +  1 \times 1) & (-1 \times 1   +   3 \times 1   +   1 \times 0) \\ \end{bmatrix} =  \begin{bmatrix} 5 & 1 \\    4 & 2 \\   \end{bmatrix} $$

H

 * $$ (AB)[i,j] = A[i,1] B[1,j] + A[i,2]  B[2,j] + ... + A[i,n]  B[n,j] \!\ $$

$$ (AB)[i,j] = A[i,1] B[1,j] + A[i,2]  B[2,j] + ... + A[i,n] B[n,j] \!\ $$