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GATE 2023 Engg. Mathematics Quiz 3
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Question 1
If 2, – 4, 3 are the eigen values of some 3 × 3 matrix A, then A–1 =
Question 2
A3x3 has an eigenvalue –1. The matrix A + I reduced to
corresponding to eigenvalue –1, all the eigenvectors of A are non-zero, then the eigenvectors of the form are __________.
![](https://gradeup-question-images.grdp.co/liveData/PROJ55161/1598525763939116.png)
Question 3
The function
satisfies the Lagrange’s Mean Value theorem in the interval (1,4) at a value of x=_________(rounded to two decimal places)
![](https://gradeup-question-images.grdp.co/liveData/PROJ36688/1567601638531179.png)
Question 4
Consider x,y,z are positive real numbers such that x + 2y + 3z = 1.
Let
is the maximum value of
, then the value of ![](https://gradeup-question-images.grdp.co/liveData/PROJ32871/1561360534938929.png)
Let
![](https://gradeup-question-images.grdp.co/liveData/PROJ32871/156136053342961.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ32871/1561360534200448.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ32871/1561360534938929.png)
Question 5
The following differential equation is an example of
Question 6
An ordinary differential equation is given below
The general solution of the differential equation is
Question 7
Find the value of ![](https://gradeup-question-images.grdp.co/liveData/PROJ24750/1547125017242783.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ24750/1547125017242783.png)
Question 8
f(z) = u (x,y) + i v(x,y) is an analytic function of complex variable z = x + i y, where i =
. If u(x,y) = 3xy, then v(x,y) may be expressed as
![](https://gradeup-question-images.grdp.co/liveData/PROJ48944/1590058220853896.png)
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