Problem: Article: You can transpose any matrix, regardless of how many rows and columns it has. Square matrices, with an equal number of rows and columns, are most commonly transposed, so we'll use a simple square matrix as an example: matrix A =1  2  34  5  67  8  9 Rewrite row one of the matrix as a column:  transpose of matrix A = AT  first column of AT:123 The second row of the original matrix becomes the second column of its transpose. Repeat this pattern until you have turned every row into a column:  AT =1  4  72  5  83  6  9 The transposition is exactly the same for a non-square matrix. You rewrite the first row as the first column, the second row as the second column, and so forth. Here's an example with color-coding to show you where the elements end up:  matrix Z =4  7  2  13  9  8  6  matrix ZT =4  37  92  81  6 The concept is pretty simple, but it's good to be able to describe it in mathematics. No jargon is required beyond basic matrix notation:  If matrix B is an m x n matrix (m rows and n columns), the transposed matrix BT is an n x m matrix (n rows and m columns).  For each element bxy (xth row, yth column) in B, the matrix BT has an equal element at byx (yth row, xth column).
Summary: Start with any matrix. Turn the first row of the matrix into the first column of its transpose. Repeat for the remaining rows. Practice on a non-square matrix. Express the transposition mathematically.

INPUT ARTICLE: Article: You can also use A4 paper. Admire your handiwork.

SUMMARY: Get a sheet of origami paper. Stand up the wolf.

In one sentence, describe what the following article is about: Regardless of the seasonings (or lack thereof) you choose to use for your flank steak, you will probably want to begin by scoring it, especially if you have a thick piece of meat. Scoring is a process in which shallow cuts are made into the surface of the steak to allow both heat and seasonings to penetrate deeper into the meat. To score your flank steak, place the flank steak on a cutting board, then use the tip of a sharp knife to make several shallow cuts into the surface of both sides of the steak in a diamond pattern. Try to make each cut about 1⁄4 inch (0.6 cm) deep. If you can, cut against the grain of the meat. As we'll eventually learn, the general rule with flank steak is to always cut against the grain to reduce the meat's toughness. If cooked correctly, flank steak can taste great without any seasoning at all. However, proper seasonings give this dish a burst of zesty flavor that can make it absolutely irresistible. When it comes to seasoning your flank steak, generally, your two options will be to use a marinade or a dry rub. Marinading your steak means letting soak in a mix of flavorful liquid ingredients so that it absorbs its flavor, while a dry rub is exactly what it sounds like — a mix of dry ingredients that you rub onto the outside of the steak. Both options can result in great flank steak. However, these seasoning methods aren't usually used together, so it's a wise idea to decide which method you're using before you start to cook.  Note that sample marinade and dry rub recipes are listed above in the "Ingredients" section. If you're using a marinade, you will want to begin early so that your flank steak has enough time to soak before cooking. Generally, you'll want to let your meat marinate for at least 2-3 hours, though marinating for as long as overnight can give stronger flavors. Whether you're using a marinade or a dry rub, the basic process for preparing each is the same. Simply combine the ingredients in a single vessel and mix thoroughly until the ingredients are combined. When you've achieved a thorough mix, your seasonings are ready to be applied to your flank steak. If you're not interested in the pair of delicious marinade and dry rub recipes listed above, it's easy to make your own. For marinades, you'll want to start with an oil base (like olive oil or vegetable oil) and add your preferred seasonings, some of which should be acidic liquids (like citrus juice or vinegar) to cut the oil. To make a dry rub, simply combine dry or powdered ingredients that you like. A good mix of sweet, salty, savory, and spicy flavors is always a good bet. If you've chosen to add flavor to your steak with a marinade, begin by pouring the marinade in to a large zip-lock bag, then add the flank steak. Squeeze most of the air out of the bag, then seal it securely shut. Knead the bag to be sure the steak is completely coated in marinade. Leave the marinating steak in its bag in the refrigerator for at least 2-3 hours; some prefer to allow the meat to marinate overnight. Note, however, that the longer you allow your meat to marinate, the stronger it will taste. If you don't have any zip-lock bags handy, you can soak your meat in a bowl covered with plastic wrap, a tupperware container, or any other plastic container with a seal. On the other hand, if you're more interested in the tasty exterior crust that a dry rub provides, skip the marinade and apply your dry rub instead. Pour your dry rub into a large bowl and drop your flank steak in. Use your hands to toss your meat in the dry rub until it is completely covered. Be generous with your dry rub — you want every surface of your flank steak to receive a thorough coating. When done, let the meat sit until it reaches room temperature, or, if you're not grilling immediately, place it on a platter in the refrigerator.
Summary:
Score your steak. Choose a marinade or dry rub for your steak. Mix your seasonings. If marinading, soak your steak. Alternatively, apply your dry rub.