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Pavleen K.

Masters Student at University of Southern California

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Linear Algebra

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Question:

What is the trick to finding the inverse of a 2d matrix quickly.

Pavleen K.

Answer:

Its actually quite simple. Just swap the numbers on the primary diagonal, that is the numbers on the top left and bottom right. And change the signs of the numbers on the secondary diagonal, that is the numbers on the top right and bottom left. So if there is 2 on the top left and 3 on the bottom right, the inverse matrix will have 3 on the top left and 2 on the bottom right. And if there is 4 on the top right and -2 on the bottom left, the inverse matrix will have -4 on the top right and +2 on the bottom left.

Geometry

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Question:

What is the surface area of a rectangle ( 10 X 4 cm sq ) folded into a hollow cylinder, along its longest side, from end to end?

Pavleen K.

Answer:

The surface area of a hollow cylinder is given by : 2*pie*r*h To find this, we need the values for 'r' and 'h'. Since the rectangle is folded along its longest side, that is 10cm, the height of the rectangle will be the height of the cylinder that is 4cm ( h ). The circles so formed at the bases of the cylinder would have a circumference equal to 10cm, since it was folded along that side. The circumference of a circle is given by : 2*pie*r We have the value for 'h', which is 4cm. We can find the value of 'r' from above. 2*pie*r = 10, r = 10 / (2*pie ) = 5/pie Which implies, the surface area of the cylinder is : 2*pie*(5/pie)*4. Which gives the answer 40 cm square!

Basic Math

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Question:

What would the answer to the following : 2 + 2 - 2 / 1 * 2 ?

Pavleen K.

Answer:

When it comes to such questions, there is one rule to follow : BODMAS. That is Brackets, Orders, Division, Mathematics, Addition and Subtraction. This rule simply talks about the order of mathematical operation implementation. That is, terms within brackets are solved first. Then terms with some power, or some Order, are solved next, ( e.g. 2 to the order of 2 is 4 ). Division and multiplication take the equal precedence, but they have to be read left to right to solve. That is whatever comes first between these two, when going from left to right, that operation should be solved next, and similarly goes for addition and subtraction. But its very important to maintain order. If the above were solved, by not considering the BODMAS, we will get : 2 + 2, that is 4. Then 4 - 2, that is 2. Then 2/1, which is 2, and finally 2*2, which is 4. But if you solve via BODMAS, since there are no brackets or orders, we will skip to division / multiplication. Since we have both of these operations, we will consider the one which comes first from left to right, which is 2/1, which is 2. Then 2*2, which gives 4. This gives Part 2 of the solution. Now for Part 1, lets jump to addition, that is 2+2, which gives 4. Now we will do Part 1 - Part 2, which is 4 - 4, and we get 0! We got different answers! That is the magic of BODMAS. If you dont believe this to be right, go ahead and google it!

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