6. (10%) Factor the matrix B into B = LDLᵀ.

$$\mathbf {B} = \left[ \begin{array}{c c c} 5 & 5 & 0 \\ 5 & 7 & 2 \\ 0 & 2 & 9 \end{array} \right]$$

7. (10%) Project \( \mathbf{b} = \begin{bmatrix} 6 \\ 7 \\ 8 \\ 9 \end{bmatrix} \) onto the column space of \( \mathbf{C} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix} \). What is the projection matrix \( \mathbf{P} \)? What is the projection \( \mathbf{p} \)?

(a) Are all the pivots of \( \mathbf{D} \) positive?

(b) Are all the upper left determinants of \( \mathbf{D} \) positive?

(c) Are all the eigenvalues of \( \mathbf{D} \) positive?

(d) Is \( x^{T}Dx \) always positive except at \( x = 0 \)?

(e) Does \( \mathbf{D} \) equal \( \mathbf{R}^{\mathrm{T}}\mathbf{R} \) for a matrix \( \mathbf{R} \) in which all the columns are independent?

III、Short Essay (20%)Please read the paragraph below and respond to the associated questions. Consider offering detailed and thoughtful answers.As a cofounder and the CEO of the U.S. chipmaker Nvidia, Jensen Huang operates in a high-velocity industry requiring agile, innovative thinking. Reflecting on how his leadership style has evolved, he told the New York Times, “I probably give fewer answers and I ask a lot more questions...It’s almost possible now for me to go through a day and do nothing but ask questions.” He continued, “Through probing, I help [my management team]...explore ideas that they didn’t realize needed to be explore(D)” (quoted from The Art of Asking Smarter Questions, Harvard Business Review, May–June 2024.)Based on the above description and what is known from the media about Jensen Huang, (1) please analyse Huang’s leadership style to align with key leadership theories and (2) explain its potential impact on innovation and team development.

IV、Short Essay (20%) In August 2024, 13 current and former TSMC(台積電)employees filed a class action lawsuit in Californi(A) The 13 plaintiffs, whose backgrounds include the US, Mexico, Nigeria, Europe and South Korea, were seeking damages to redress TSMC’s apparent discrimination practices. In the lawsuit, the plaintiffs claimed TSMC’s employment practices include an “intentional pattern and practice of employment discrimination against individuals who are not of East Asian race, not of Taiwanese or Chinese national origin, and who are not citizens of Taiwan or China, including discrimination in hiring, staffing, promotion, and retention/termination decisions.” While declining to comment on the lawsuit, TSMC did say that recruitment and promotion in the company did not take into account factors such as nationality and rac(E) “TSMC believes strongly in the value of a diverse workforce, and we hire and promote without regard to gender, religion, race, nationality, or political affiliation because we respect differences, and believe that equal employment opportunities strengthen our competitiveness,” the company sai(D) “We also provide various channels for employees to raise concerns, and strive to address concerns constructively,” it sai(D)(Source: Taipei Times, Friday Nov 15, 2024) Imagine you are a consultant hired by TSMC to improve its diversity and inclusion efforts. Based on the lawsuit allegations, list, explain and identify potential issues with TWO specific recommendations that TSMC could implement in its organizational structure and processes to mitigate unconscious bias in hiring, promotion, and performance evaluation.

1. 領導風格理論 (25 分)請從以下幾個關鍵詞來說明單構面的領導風格理論：(1)權威式；(2)民主式；(3)放任式；(4)民主諮商式；(5)民主參與式；(6)仁慈專制式；(7)連續構面。

(1) 請問何謂企業社會責任(corporate social responsibility, CSR)? CSR 興起的背後原因為何？

115年 - 115 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147267

114年 - 114 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147271

114年 - 114 國立臺北大學_碩士班一般入學考試試題_民俗藝術與文化資產研究所：語文論述能力(民俗與文化)#147240

113年 - 113 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147270

113年 - 113 國立臺北大學_碩士班一般入學考試試題_民俗藝術與文化資產研究所：語文論述能力(民俗與文化)#147238

112年 - 112 國立臺北大學_碩士班一般入學考試試題_民俗藝術與文化資產研究所：語文論述能力(民俗與文化)#147239

111年 - 111 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147257

111年 - 111 國立臺北大學_碩士班一般入學考試試題_民俗藝術與文化資產研究所：語文論述能力(民俗與文化)#147245

111年 - [無官方正解]111 國立臺北大學_碩士班一般入學考試試題_金融與合作經營學系：合作經濟學#147235

110年 - 110 國立臺北大學_碩士班一般入學考試試題_資訊工程學系：線性代數與離散數學#147277