IISc Bangalore CDS (M.Tech. Course Work) Interview Experience 2021

Question

Primary Interactions:

• First, they have read out my application, asked about the choices and preference order of departments.
• Then I was asked about my GPA.
• Next, they asked me about my future plans and favourite subjects.

Questions:

1. All the elements of a NxN matrix are 1. Can you guess at least one eigen value, quickly? Give reason in support of your answer.
2. I is an identity matrix of size NxN. U is a column vector of size Nx1. It is given, $U^TU\neq O$ and $UU^T$ is of size NxN. The following equation holds: $[I - \alpha [UU^T]]U = - U$ where $\alpha$ is a scalar. Find the value of scalar $\alpha$ and also show the derivation.
3. Write an efficient algorithm to find out the multiplication of a Diagonal Matrix and an Anti-diagonal matrix of size NxN. 

GATE Score (2021): 646   

GPA: 9.53 (Linear Average upto 6th Semester, during the time of interview)

Category: SC

Result: Selected

Comments

Congratulations 👍

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Congratulations bro. Is the ans of Q2) 2 ? May you kindly confirm?

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Can you explain bro?

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@Sriram_24

I did some mistake and got that answer, forgot to remove that from here
I think the question is missing some more data, possibly 'U' is orthogonal UU^T=I

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That's cool! The data you mentioned will help to get the answer!

Thank you!

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at least one eigen-value is zero .because determinant of matrix is zero.

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1) eigenvalues: N and 0,0,...0 (N-1)times
2) i'm getting alpha value 2.

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Can someone explain question 2