14 Additional Exercises
Exercises
Typeset the following.
1. [latex]a<b[/latex]
2.
\begin{bmatrix} 6 & \frac{1}{2} & 0 \\ 7 & 5 & 10 \\ 0 & 17 & 0 \end{bmatrix}
3. [latex]\left\{\frac{ab}{c}\right\}[/latex]
4. [latex]\{\frac{ab}{c}\}[/latex]
5.
[latex]\begin{align} a_{11} + b_{11}& = c_{11}& a_{12}& =b_{12}\\ b_{21}& = c_{21}& a_{22}& =b_{22}+c_{22} \end{align}[/latex]
6.
[latex]\begin{align} a& =b+c-d\\ & \quad +e-f\\ & =g+h\\ & =i \end{align}[/latex]
7. \begin{align}
x&=y & X&=Y & a&=b+c\\
x’&=y’ & X’&=Y’ & a’&=b\\
x+x’&=y+y’ & X+X’&=Y+Y’ & a’b&=c’b
\end{align}
8. \begin{align}
x& = y_1-y_2+y_3-y_5+y_8-\dots
&& \text{by 6.6}\\
& = y’\circ y^* && \text{by 7.5}\\
& = y(0) y’ && \text {by Axiom 1.}
\end{align}
9. \begin{align}
A_1&=N_0(\lambda;\Omega’)-\phi(\lambda;\Omega’),\\
A_2&=\phi(\lambda;\Omega’)-\phi(\lambda;\Omega),\\
A_3&=\mathcal{N}(\lambda;\omega).
\end{align}
10.
[latex]\left( \begin{array}{cc} 2\tau & 7\phi-\frac{5}{12} \\ 3\psi & \frac{\pi}8 \end{array} \right) \left( \begin{array}{c} x \\ y \end{array} \right) \mbox{and} \left[ \begin{array}{cc|r} 3 & 4 & 5 \\ 1 & 3 & 729 \end{array} \right][/latex]
11. Equation [latex]\sum_{i=0}^{\infty} a_i x^i[/latex] is a typical power series.
