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Elementary Matrices GATE 2024 Fundamental Quiz
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Question 1
The eigen vector of the matrix
is written in the form
and
. What is the value of a + b?
![](https://gs-post-images.grdp.co/2022/6/11-img1654073457116-71.jpg-rs-high-webp.jpg)
![](https://gs-post-images.grdp.co/2022/6/12-img1654073457134-23.jpg-rs-high-webp.jpg)
![](https://gs-post-images.grdp.co/2022/6/13-img1654073457134-88.jpg-rs-high-webp.jpg)
Question 2
Suppose that there is a matrix
. For what value of k, the given matrix has positive eigen values?
![](https://gradeup-question-images.grdp.co/liveData/PROJ98469/1644296758042680.png)
Question 3
Given the matrix:
The value of trace of the matrix is ___________.
Question 4
If
. Then the determinant of
_____________.
![](https://gradeup-question-images.grdp.co/liveData/PROJ85523/1626936429322648.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ85523/1626936430078396.png)
Question 5
If
is
non singular matrix such that
and
, then
equals :
![](https://gradeup-question-images.grdp.co/liveData/PROJ84208/1626156345124320.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ84208/1626156345817213.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ84208/1626156346480882.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ84208/1626156347238666.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ84208/1626156347896134.png)
Question 6
Determine the rank of the matrix:
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Jun 21GATE & PSU CS