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Question,A,B,C,D,Answer |
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"假設矩陣 |
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\[\begin{bmatrix}1&2&3&1&b\\2&5&3&a&0\\1&0&8&6&c\end{bmatrix}\] |
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可以被轉換成簡化行階梯形式 |
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\[\begin{bmatrix}1&0&0&-2&0\\0&1&0&d&-1\\0&0&1&1&e\end{bmatrix}\] |
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以下哪些等式是正確的？",\(a=1\),\(d=-1\),\(b=3\),\(e=2\),C |
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"因數\(f(t)=2\cos(3t)\),\(0\leqt\leq\frac{\pi}{3}\)，若在\(t=0\)處,f(t)的傅立葉餘弦級數（Fouriercosineseries）收斂到A，傅立葉正弦級數（Fouriersineseries）收斂到B；在\(t=\frac{\pi}{3}\)處，f(t)的傅立葉餘弦級數（Fouriercosineseries）收斂到C，傅立葉正弦級數（Fouriersineseries）收斂到D。則A,B,C,D各值為何？","A=2,B=0,C=-2,D=0","A=2,B=0,C=2,D=01","A=0,B=0,C=0,D=0","A=0,B=2,C=-2,D=0",A |
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"下列哪一個是下方方程式的解？ |
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\[\begin{bmatrix}1&2&3&1\\2&2&1&2\\3&1&1&3\\1&2&3&2\end{bmatrix}\begin{bmatrix}1&2&3&4\\5&6&7&8\\0&0&0&0\\9&10&11&12\end{bmatrix}+\begin{bmatrix}1&-2&-3&-1\\-2&2&1&-2\\-3&1&1&3\\-1&-2&3&-2\end{bmatrix}\begin{bmatrix}1&2&3&4\\5&6&7&8\\0&0&0&0\\9&10&11&12\end{bmatrix}=?\]",\[\begin{bmatrix}2&4&6&8\\20&24&28&32\\64&72&80&88\\0&0&0&0\end{bmatrix}\],\[\begin{bmatrix}2&4&6&8\\20&24&28&32\\64&76&88&80\\0&0&0&0\end{bmatrix}\],\[\begin{bmatrix}2&4&6&8\\20&24&28&32\\64&72&88&80\\0&0&4&0\end{bmatrix}\],\[\begin{bmatrix}2&4&6&8\\20&24&28&32\\64&72&88&80\\0&0&0&0\end{bmatrix}\],A |
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\(\lim_{x\to\infty}(\sqrt{x^2+11x}-x)=?\),\(37\),\(\frac{111}{4}\),\(\frac{11}{2}\),\(\frac{111}{5}\),C |
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"設函數\(f(x)=\begin{cases}-1,&-\pi<x<0\\1,&0<x<\pi\end{cases}\)且\(f(x+2\pi)=f(x)\)，將此函數展開(Fourierseries)展開成\(\frac{4}{\pi}(a\sin{x}+b\sin{2x}+c\sin{3x}+d\sin{4x}+\ldots)\)，則\(a+b+c+d=\)？",2,3,1,4,D |
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