Dear student

It's a quite simple question and can be answered in many ways.

First let me explain. We will start with giving everyone an equal amount,  20/5=4.

Now, we have to divide it such that each numbers freqYancy changes from even to odd.

For that we will decrease and increase in certain amount and after that you can get many answers like this one.

5,3,5,7

Hello,

Hope you're doing well.

Let equation 2x + 3y = 8 -(1)

And equation -3x + 2y = -1 -(2)

Now multiplying the equation (1) by 3 and equation (2) by 2.

On multiplying we get,

6x + 9y = 24

-6x + 4y = -2

Now adding the equations. On adding we get,

13y=22 so y =22/13

Now putting the value of y in equation (1)

We get the value of x: 2x +3(22/13) = 8

2x = 8- 66/13

2x= 38/13

X = 19/13

The sum of all the eigenvalues of a matrix is equal to the trace of the matrix. And since the matrix is real, the trace should also be a real value. Which further implies that the sum of all the eigenvalues should be a real number. So, add all the three eigenvalues and check which option is giving the sum a real number. So, checking all the options, you get that no option can be correct answer. However, if you do option b as (1, -i) then it can be the correct answer.

Hope this helps.

Hello,

Linear algebra is an important part of engineering mathematics in Gate exam. Matrices and determinants are the basic concepts of linear algebra. Without them you cannot Excel at linear algebra. So you have to look at linear algebra as a whole. You must be good at matrices and determinants. Engineering Mathematics questions are compulsory and carry 15% of the total weightage (15 Marks).

Best of luck!!

Hello there

To write the give lpp into standard form a few things have to be done.Since x3 is unrestricted in sign it should be into a format where its not.A slack variable should be introduced in the second condition.So the standard form would be

Min z=2x1+7x2+r1-s1

St x1+r1=7

3x1+x2-s1=2

x31-x32>=0

For further clarification just comment below.You can clear your doubts by watching NPTEL videos of Linear Programming and Simplex Method on YouTube.

Hope I was able to help.

Dear user,

Let, the given matrix be A.

1             0             0             0             1

0             1             1             1             0

A   =       0             1             1             1             0

0             1             1             1             0

1            0             0             0             1

To find eigen value,

Put, A    = (lambda) (I) ₅

=> A – (lambda) X (I) ₅ = 0

|1 0 0 0 1|                           |1 0 0 0 0|

|0 1 1 1 0|                           |0 1 0 0 0|

|0 1 1 1 0| - (X)     |0 0 1 0 0|  = 0

|0 1 1 1 0|                           |0 0 0 1 0|

|1 0 0 0 1|                           |0 0 0 0 1|

Thus,

1-X         0             0             0             1

0             1-X         1             1             0

0             1             1-X         1             0        = 0

0             1             1             1-X         0

1            0             0             0             1-X

Now, take determinant value

=> -x ⁵ + 5x ⁴ – 6x ³ = 0

=> -x ³ (x ² - 5x + 6) = 0

=> x ³ (x ² – 3x - 2x + 6) = 0

=> x ³ ((x - 3) -2(x - 3)) = 0

Thus,

=> x ³ (x-3)(x-2) = 0

=> x = 0, x = 3, x=2

Now, since x is not = 0 as per question

Thus, valid eigen values are: 2,3.