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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 __________.

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)

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

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

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
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