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851 Views

How do you divide twenty mangoes among five people so that each gets mango or mangoes in odd numbers?

Pratyaksha Goswami 22nd Oct, 2020

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

61 Views

find x and y. 2x+3y=8 and -3x+2y =-1

Shreya sharma 14th Oct, 2020

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



2373 Views

A(3*3) real matrix has an eigenvalue i, then its other two eigenvalues can be? a)0,1 b)-1,i c)2i,-2i d)0,-2i

Rishi Garg 13th Jul, 2020

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.

77 Views

sir,what are topics in linear algebra for GATE exam...

Akash saw 6th Feb, 2020

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!!

261 Views

convert the following linera program into standard form: minimize 2x1+7x2 subject to x1=7 3x1+X2>=24 x2>=0 x3<=0

Rohit 12th Dec, 2019

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.

596 Views

The product of non-zero eigen values of the matrix is..... 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1

anshika.verma2019 20th Nov, 2020

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.

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