Last edited by @suen 2024-10-11T09:59:58Z
1. Determinant of the 4x4 matrix
We need to find the determinant of the matrix:
\begin{bmatrix}
2 & 1 & 4 & 1 \\
3 & -1 & 2 & 1 \\
5 & 0 & 6 & 2 \\
1 & 3 & 0 & 3
\end{bmatrix}
Using cofactor expansion (expansion by minors), we can expand along the first row:
\text{det}(A) = 2 \times \text{det}\begin{bmatrix} -1 & 2 & 1 \\ 0 & 6 & 2 \\ 3 & 0 & 3 \end{bmatrix}
- 1 \times \text{det}\begin{bmatrix} 3 & 2 & 1 \\ 5 & 6 & 2 \\ 1 & 0 & 3 \end{bmatrix}
+ 4 \times \text{det}\begin{bmatrix} 3 & -1 & 1 \\ 5 & 0 & 2 \\ 1 & 3 & 3 \end{bmatrix}
- 1 \times \text{det}\begin{bmatrix} 3 & -1 & 2 \\ 5 & 0 & 6 \\ 1 & 3 & 0 \end{bmatrix}
We calculate each of the 3x3 determinants individually and sum the results. Since this involves many calculations, I’ll compute the exact value for you.
2. Limit problem:
We are given:
\lim_{{x \to \infty}} \frac{{2x + 1}}{x}
First, simplify the expression:
\frac{{2x + 1}}{x} = \frac{2x}{x} + \frac{1}{x} = 2 + \frac{1}{x}
As $$(x \to \infty), (\frac{1}{x} \to 0)$$. Therefore, the limit is:
\lim_{{x \to \infty}} \left( 2 + \frac{1}{x} \right) = 2
So, the answer to the limit problem is 2.
Let me compute the determinant of the 4x4 matrix for you.
The determinant of the given 4x4 matrix is approximately 0 (more precisely, a very small number close to zero, $$(-1.998 \times 10^{-14})$$ , which is essentially zero due to numerical precision).
Thus, the determinant is 0.
Summary of solutions:
- Determinant of the matrix: (0)
- Limit: (2)
gpt依旧智障 算个三阶行列式都算不明白
现在已经是靠脚本一秒10题了 
1 Like
难绷。最近室友疯狂迷恋上这种幼稚而无聊的东西，感觉现在人太缺少成就感和获得感了，他们甚至要到这里找胜利的感觉
2 Likes
就要
你別拷打我錯了哥我得反省
為什麼我要炸魚炸魚能贏嗎會贏的5以內比大小會為我們帶來勝利
20以內比大小贏不了
會贏嗎如果不能玩小猿口算的話，瓦塔西你這個人啊，腦子裏只想著小猿口算呢從來沒覺得被三秒速通開心過
数学大神啊
@Smarty
算一下上面的题
我们班同学已经开始玩这个上瘾了
笑死我了，今天预科部升旗又cue了下“小猿口算的所谓狂欢”
3 Likes
说啥了
让我们不要被企微群聊的闲聊和小猿口算的“狂欢”诱惑
《一年级》
中国教育是这样的，感觉一直在要求着一种禁止娱乐，限制休息的苦行僧一样的模式
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难绷……
歌颂苦难，比苦大赛