1. Given : 2x1 - x2 + 3x3 = 11 x1 + 2x2

1. Given : 2x1 - x2 + 3x3 = 11 x1 + 2x2 - 2x3 = -3 -x1 + 3x2 + 4x3 = -5 a. Write the augmented matrix b. Using Elementary Row Operations method, find the solution for given equations above. 2. Find the solution of this equation x + 2y - z = 5 3x + y - 2z = 9 -x + 4y + 2z = 0 3. Calculate x, y and z 8y + 16z = 0 x - 3z = 1 -4x + 14y + 2z = 6 4. Using Gaussian Elimination by Back Substitution, solve the following problems a. -2y + 3z = -83 -4x + 5y - 6z = 203 7x - 8y + 9z = -323 b. -9x - 8y - 7 = -119 6x + 5y + 4z = 80 -3x + 2y - z = -65

Transcript

00:01 Hi everyone, welcome to the question.

00:03 So in this question, just given that perimeter of the field is 400.

00:07 Now we have to find a length and breadth of the rectangular part of the field.

00:12 So coming to the question.

00:15 So here in the diagram, if you see, it's a rectangular field with two semicircles on both sides.

00:21 So let's take x to be the length and y to be the breadth.

00:25 So let length be x and breadth.

00:34 Breadth b y so from this we can write the perimeter of the field is equal to so perimeter of the field is equal to there are two length right so two x here there is one length and here is one length so two x now there are two semicircles this side and this side so one semicircle so we will write this as two x plus 1 divided by 2 pi y plus 1 divided by 2 pi y so how did this come so we have used the perimeter of the semicircle formula so perimeter of the semicircle is equal to 1 by 2 pi d so here if you see pi value is same so 1 divided by 2 pi and the d is the die is the die so here the diameter is actually the breadth right it is y so y so that's how we have got this half 1 by 2 pi y plus 1 by 2 pi y so now from this we can write perimeter so the perimeter we have they have given us as 400 so 400 is equal to 2x plus so 1 by 2 pi y plus 1 by 2 pi y plus 1 by 2 pi y plus 1 by 2 pi y plus 1 by is equal to we can write this as pi multiplied by y so pi multiplied by y is equal to 400 minus 2x so y is equal to 400 minus 2x divided by pi let's take this to be our first equation now area of the rectangular field now we know the area formula as area of a rectangle is equal to length multiplied by breath so area is equal to as like length we have taken it to be x multiplied by breath we have taken to be y so a is equal to so x multiplied by y we have found so you will substitute the first equation here that is 400 minus 2x divided by pi so from this we can get a is equal to 400 x minus 2 x to the part 2 divided by pi now we are going to differentiate a differentiating a with respect to x so you would get a dash of x is equal to 1 divided by pi is constant so 400 minus 4 x so now a dash of x should be equated to 0 so we would get 1 .5 divided by pi multiplied by 400 minus 4 x is equal to 0 so from this we can write 400 minus 4x is equal to 0 and 400 is equal to 4x so x is equal to 100 now we can substitute this x value 100 in our first equation so from 1 we would get y is equal to 400 minus 2 multiplied by 100 divided by so that is equal to 200 divided by pi.

04:22 So y value is 63 .694...

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