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ESE 2021 Technical Quiz || Linear algebra(I & II)
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Question 1
Consider the following statements:
1) The rank of a matrix is the order of largest non-vanishing minor of A.
2) For any two matrices A & B, ρ(AB) ≥ min {ρ(A), ρ(B)}.
3) For any two matrices A and B, ρ(A+B) ≤ ρ(A)+ρ(B).
Which of the following statements is/are correct?
Question 2
Consider matrix
, then determinant of Adj (Adj A) is _________.
![](https://gradeup-question-images.grdp.co/liveData/PROJ46339/1585049862761711.png)
Question 3
The rank of matrix
is ___________.
![](https://gradeup-question-images.grdp.co/liveData/PROJ46420/1585134598808693.png)
Question 4
Consider the system of linear equation:
2x2 + x3 = – 2
3x1 + 5x2 – 5x3 = 1
2x1 + 4x2 – 2x3 = 2
The above system has _________.
Question 5
If two eigen values of matrix
are 0 and 6, then the eigen vector corresponding to the largest eigen value of A is:
![](https://gradeup-question-images.grdp.co/liveData/PROJ49219/1614062119542575.png)
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Jun 20ESE & GATE EE