SIT787: Mathematics for AI Assignment Help
Question
SIT787: This is a question-and-answer-based assessment for the Deakin University Australia. The students are required to demonstrate their understanding related to the application of mathematical formulas for AI-based learning. A handwritten submission needs to be made by the student by depicting the answers using quotients and surds.
Solution
This solution for this second assessment for the Mathematics for AI course incorporates a well-explained answer file using mathematical formulas and concepts. The solution to all three questions is completed by our experts.
Question 1
For this question, u, v, and w vectors are provided for which sub-questions need to be answered using appropriate calculations. Our experts have provided handwritten answers to all the solutions.
- Based on these standards, the student is supposed to identify which two vectors are most similar to one another.
- Secondly, the student needs to identify which two vectors are most similar to one another on the basis of their cosine similarity.
- Here, our experts have provided the justification behind the difference in answers for the above two questions.
- Lastly, this sub-question delves into a way through which this difference can be corrected along with proposing the result if this correction is done.
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Question 2
An incomplete matrix is provided to the students in the assessment file with certain unknown entries. The following sub-questions need to be answered based on this question. We have provided some snippets of the complete solution written by our experts.
- This sub-question demands the student to find A’s rank by determining the values of the unknown values in the matrix.
- Next, the number of eigenvalues A based on the different values of the unknown quantities have been identified here.
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Question 3
This question also presents a matrix value. The student needs to assess this matrix and answer the sub-questions that are provided below. Our experts have approached all these solutions using careful analysis and knowledge of the mathematical principles related to AI.
- In this sub-question, the student is required to create B = AT A. Our experts have calculated the eigenvalues and eigenvectors of B based on this construction.
- Next, the number of eigenvalues A based on the different values of the unknown quantities have been identified here.
- In this question, matrix D needs to be constructed.
- Through this question, the student is urged to determine the eigenvectors of C=AAT.
- Here u1, u2, and u3 are determined by our experts.
- The product U DVT is calculated in this sub-question.
- In this last sub-question, the basis for C(A), C(AT), N(A), and N(AT) for matrix A is determined by our experts. Through a thorough analysis, it is also outlined what can one say about the bases for the four subspaces of matrix A in terms of the columns U and V.
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