Hello learners In this article we are going to discuss NPTEL Machine Learning for Engineering and science applications Assignment 1 Answers. All the Answers provided below to help the students as a reference, You must submit your assignment with your own knowledge and use this article as reference only.
About the course:-
Recent applications of machine learning have exploded due to cheaply available computational resources as well as wide availability of data. Machine Learning (ML) techniques provides a set of tools that can automatically detect patterns in data which can then be utilized for predictions and for developing models. Developments in ML algorithms and computational capabilities have now made it possible to scale engineering analysis, decision making and design rapidly.
NPTEL Machine Learning for Engineering and science applications Assignment 1 Answers 2024:
1. The animated movie Kung Fu Panda 2 used Dolby 7.1 Surround Sound which uses 8 audio channels. Consider an audio clip put together from all 8 channels, resulting in a matrix of dimensions 1024×8. The output of this audio stream is to be converted to a 2 channel stream while retaining the length of the audio clip. So, a matrix transformation is applied on the source to convert it into a 2 channel stream. The sizes of the final output matrix and the transformation matrix would be:
Answer :- c
2. Consider the vectors aN×1 and bN×1. If IN×N is the identity matrix of size N×N then the determinant of the matrix I+abT is given by:
Answer :- a
3. Consider a 5×5 matrix A with the following eigen values (−1,1,0,−2,2). What would be the eigen values of the matrix A−1?
Answer :- d
4. The solution to the system of equations given by :
Answer :- b
5. Consider an orthogonal matrix A with ATA=I. If we define a vector y=Ax, where x is a column vector, which of the following are true about ∥y∥ (where ∥y∥ is the L2-norm of y)?
Answer :- d
6. Consider two matrices, A and B, where A is a 3×4 matrix and B is a 4×3 matrix. We perform the following operations sequentially:
i. Compute of the product of A and B, resulting in matrix C.
ii. Take transpose of the matrix C.
iii. Perform an element-wise (Hadamard) product of the transposed matrix C with a 3×3 identity matrix.
iv. Add a 3×3 matrix D, all of whose elements have the value 2.
What is true about the resulting matrix after performing the above operations?
Answer :- b
7. Consider three vectors in R3:
v1=⎡⎣⎢10−1⎤⎦⎥,v2=⎡⎣⎢011⎤⎦⎥,v3=⎡⎣⎢110⎤⎦⎥
Are these vectors linearly independent?
Answer :- b
8. In an experiment, data is represented by a matrix M, which records the interaction intensities between four different particles. The matrix is given as:
M=⎡⎣⎢⎢⎢35947210846151836⎤⎦⎥⎥⎥
The trace of the matrix M is used to calculate the total intensity of self-interactions among particles. You are also given the transpose of the matrix M, denoted as MT. What is the relationship between the total intensity of self-interactions calculated using M and MT?
Answer :- c
9. Consider the following 3×3 matrix:
C=⎡⎣⎢142254366⎤⎦⎥
Is the matrix C invertible?
Answer :- d
10. Consider the vector v=⎡⎣⎢⎢⎢⎢⎢⎢−3401−2⎤⎦⎥⎥⎥⎥⎥⎥. For which of the following norms will the norm of vector v be the minimum?
Answer :- c
