# Tutor profile: Hiren M.

## Questions

### Subject: Linear Algebra

Solve the given equations and find value of x, y and z x + 2y = 1 3x + 2y + 4z = 7 −2x + y − 2z = − 1

First lets list all equations x + 2y + 0z = 1 ..........(i) 3x + 2y + 4z = 7........(2) -2x + y - 2z = -1........(3) As we can see we have 2y common in equation 1 & 2 so subtract equation 1 from 2 we get (x + 2y + 0z) - (3x + 2y + 4z) = 1 - 7 x = 3 - 2z....................(4) Multiplying equation (3) by 2 and add it with equation (2) so as to eliminate 4z 2(-2x + y - 2z ) + (3x + 2y + 4z) = 2(-1) + 7 we get x = 4y - 5...................(5) Comparing equation (4) and (5) we get 3 - 2z = 4y - 5 z = 4 - 2y..................(6) Hence now we have got new set of equations (4), (5) and (6) having two variables Substituting equation (5) in (1) we get (4y-5) + 2y = 1 y = 1 Substituting value of y in equation (6) z = 4 - 2(1) z = 2 Substituting value of z in equation (4) x = 3 - 2(2) x = -1 Hence value of x ,y and z is (-1), 1 and 2 respectively.

### Subject: Basic Math

Find mean median and mode of the given data {87, 56, 69, 87, 93, 82}

Mean: Mean is nothing but an average value of the data. Given by sum of all the data values divided by the number of values. mean = (sum of all the data values) / (number of values) = (87 + 56 + 69 + 87 + 93 + 82 ) /6 = (474) / 6 = 79 Meadian The median is the middle number of your data set when it is ordered from least to greatest. Hence first we put the data in order from least to greatest here (56, 69, 82, 87, 87, 93) Here there are two middle numbers the 3rd and 4th which is 82 and 87. hence we take average of both (82+87) / 2 = 169/2 = 84.5 Meadian = 84.5 Mode Mode is the number in the list that occurs the most frequently Since here 87 number appears twice and each of the other numbers appears only once. Mode = 87

### Subject: Algebra

A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be ?

Let say currently the age of father ='x' and of son = 'y' as per given condition x+y= 60 Therefore x=60-y Six years ago father's age = (x-6) and son's age = (y-6) as per given condition (x-6)=5*(y-6) x-6=5y-30 x-5y= -30+6 x-5y= -24 substituting x=60-y in above equation 60-y-5y= -24 60-6y= -24 60+24= 6y 84=6y y=14 Hence present age of son = 14 years Therefore six years from now son's age = 14+6 =20 years

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