111年清華大學（後西醫） — 資訊科學

共 30 題 · 含 AI 詳解

#1 Let… › #2 Let $A, B, C, D$ be four $n$ by $n$ nonsingular matrices. What is the determinan… › #3 Let $D$ be the differentiation operator on P$^3$, the set of real polynomials wh… › #4 Let $A$ be an $m$ by $n$ matrix. Which statement is TRUE? › #5 Suppose $A=\begin{bmatrix}1&-2&3\\-2&4&2\\3&-6&1\end{bmatrix}$ and… › #6 Let $b_1=(1,0,-1,0,0), b_2=(1,1,1,1,1), b_3=(1,0,1,2,1)$ in $\mathbb{R}^5$ and $W=\text{span}\{b_1,b_2,b_3\}$… › #7 Suppose $A=\begin{bmatrix}1&2\\-2&1\\2&0\end{bmatrix}$ and $b=\begin{bmatrix}1\\8\\3\end{bmatrix}$… › #8 Suppose $A=\begin{bmatrix}1&2&0&0&3\\b&a&2b&c&2\\1&-1&5&c&-5\\a&2b&1&3&4\end{bmatrix}$… › #9 Find the largest singular value of the matrix $M=\begin{pmatrix}4&11&14\\8&7&-2\end{pmatrix}$… › #10 Fill in a complex number, $c$, such that the matrix below is unitarily diagonali… › #11 Find the parabola $y = a + b x + c x^2$ that comes closest (least squares error)… › #12 Let $S$ be the set of all positive real numbers. Now, we want to make $S$ as a v… › #13 Which of the functions $T : \mathbb{R}^3 \to \mathbb{R}^2$ is NOT a linear trans… › #14 Let $A, B\in\mathbb{R}^{3\times3}$ be square matrices. Suppose the determinants… › #15 For square matrices $A$ and $B$, we say that $B$ is similar to $A$ if there exis… › #16 Suppose that $X$ and $Y$ are exponential random variables that are independent o… › #17 Suppose that the joint cumulative distribution function of the lifetimes of two… › #18 Suppose that the random variables $X_1, X_2,...$ are independent of each other.… › #19 If $Y$ is uniformly distributed over $[0, 5]$, what is the probability that the… › #20 The moment generating function of $X$ is given by $M_X(t)=e^{2e^t-2}$ and that o… › #21 A smooth-surface table is ruled with equidistance parallel lines, a distance $D$… › #22 Consider the set of all families with two children. Randomly select one family.… › #23 Recently, Larry taught his daughter Emily how to play a game. To encourage Emily… › #24 There are 2 exams in Statistics class. The midterm score (X) is approximately no… › #25 Suppose we are interested in the rate ($p$) of Cancer A in rats that have been f… › #26 In a statistics exam, all problems are multiple-choice with 5 possible items (5選… › #27 Suppose $X_i$ independently follows a Poisson distribution with mean 3 for $i = 1 \sim 1000$… › #28 Suppose we want to investigate the relationship between the heights of students… › #29 According to the following plots of three variables X1, X2, and Y from the data… › #30 The following is a joint probability table between two categorical variables, th… ›