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\end{matrix}";i:1;s:142:"<img class="tex" alt="\begin{matrix} x &amp; y \\ z &amp; v&#10;\end{matrix}" src="/images/math/b/9/9/b99890966e1b997497211428f8e3419d.png" />";}i:165;a:2:{i:0;s:44:"\begin{vmatrix} x & y \\ z & v
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& \ddots & \vdots \\ 0 & \cdots &
0\end{bmatrix} ";i:1;s:210:"<img class="tex" alt="\begin{bmatrix} 0 &amp; \cdots &amp; 0 \\ \vdots&#10;&amp; \ddots &amp; \vdots \\ 0 &amp; \cdots &amp;&#10;0\end{bmatrix} " src="/images/math/8/1/a/81a12a09ac84853e3d25323b8643c630.png" />";}i:168;a:2:{i:0;s:44:"\begin{Bmatrix} x & y \\ z & v
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\end{pmatrix}";i:1;s:144:"<img class="tex" alt="\begin{pmatrix} x &amp; y \\ z &amp; v&#10;\end{pmatrix}" src="/images/math/4/4/4/444df88e616def4e275b4e920c7b872e.png" />";}i:170;a:2:{i:0;s:63:"
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
";i:1;s:175:"<img class="tex" alt="&#10;\bigl( \begin{smallmatrix}&#10;a&amp;b\\ c&amp;d&#10;\end{smallmatrix} \bigr)&#10;" src="/images/math/c/d/4/cd49bbc188dce0f93fef57312af5a106.png" />";}i:171;a:2:{i:0;s:104:"f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases} ";i:1;s:216:"<img class="tex" alt="f(n) =&#10;\begin{cases}&#10;n/2, &amp; \text{if }n\text{ is even} \\&#10;3n+1, &amp; \text{if }n\text{ is odd}&#10;\end{cases} " src="/images/math/9/8/5/98503cc6876b22f5900297971fdd42ed.png" />";}i:172;a:2:{i:0;s:66:"
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}
";i:1;s:182:"<img class="tex" alt="&#10;\begin{align}&#10;f(x) &amp; = (a+b)^2 \\&#10;&amp; = a^2+2ab+b^2 \\&#10;\end{align}&#10;" src="/images/math/2/c/5/2c50960e8bcfd9e86527a123a0c43aa2.png" />";}i:173;a:2:{i:0;s:73:"
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}
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z & = & a \\
f(x,y,z) & = & x + y + z
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z & = & a \\
f(x,y,z) & = & x + y + z
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\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
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\rfloor \quad \left \lceil \frac{c}{d} \right \rceil" src="/images/math/1/4/c/14c563a841b6c01dd13c5f3fa90845a1.png" />";}i:192;a:2:{i:0;s:37:"\left / \frac{a}{b} \right \backslash";i:1;s:125:"<img class="tex" alt="\left / \frac{a}{b} \right \backslash" src="/images/math/2/f/3/2f3c5907c0a4fc4fda69eb71890ce952.png" />";}i:193;a:2:{i:0;s:152:"\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow";i:1;s:240:"<img class="tex" alt="\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow" src="/images/math/d/e/7/de73c9252b269fb79408d6f791b5c3de.png" />";}i:194;a:2:{i:0;s:20:"\left [ 0,1 \right )";i:1;s:108:"<img class="tex" alt="\left [ 0,1 \right )" src="/images/math/a/3/8/a38771eae1778d0e214f6596a8dc1337.png" />";}i:195;a:2:{i:0;s:27:"\left \langle \psi \right |";i:1;s:115:"<img class="tex" 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