This hopper recipe uses either toddy, an alcoholic palm wine, or baking soda. While toddy is more traditional and adds a special flavor, both methods involve fermenting the batter overnight, producing a noticeably different flavor than the faster yeast method. . You can use any variety of rice for this recipe. Since you need to start making these hoppers the day before, you could make a pot of rice for dinner that day and save a handful (or two large spoonfuls) in a closed container in the fridge. Use 1.5 cups of rice (350 mL).While you may be used to rice that doesn't require soaking, this recipe calls for blending the rice with other ingredients, so you'll need to soak it until it is soft enough to grind or put in a food processor. Strain the soaked rice through a mesh or cloth to drain the water, leaving softened but uncooked rice. This will take a lot of work by hand, so use a blender or food processor if you have one. Blend the uncooked rice along with the grated coconut and cooked rice to a smooth or nearly smooth batter. A slightly coarse or grainy texture is fine. Add water little by little to the batter if it looks dry or you're having trouble grinding it. Stir the batter together to get a wetter, thinner mixture. Use a cooking pot or other cooking container. You'll cook this mixture and use it to start the batter fermenting, which adds air and flavor to the hoppers. Stir the batter water mixture vigorously as you heat it at a low temperature. It should continue to thicken until it is gelatinous and transparent. Remove the mixture from heat and let it sit until it reaches room temperature. Stir together thoroughly until there are no lumps. Add a little bit of water as you go if the mixture is too dry to stir. Use a large bowl with plenty of space for the batter to expand. Cover the batter mixture with a cloth or lid and let it sit at room temperature. Often, people will leave it overnight and make hoppers for breakfast in the morning. The batter should nearly double in size, and appear bubbly. Once the batter is ready, add 1 tsp (5 mL) salt and 2 tsp (10 mL) sugar, or according to taste. Add either 1/4 tsp (1.2 mL) baking soda or a splash of toddy, also known as palm wine. Toddy has a strong flavor, so you may want to start with as little as 1 tsp (5 mL) and increase the amount if the first hopper doesn't have a distinct sour flavor. Toddy is alcoholic, but the small amount used in this recipe should not affect sobriety. The batter should be thinner than American pancake batter. Add water or coconut milk until it is thin enough to easily swirl round the pan, but thick enough to stay together and not become entirely liquid. Stir or blend until there are no lumps. Use a cloth or paper towel to rub a small amount of oil across a hopper pan, wok, or skillet to lightly grease it. Heat for a couple minutes over medium heat; the pan doesn't need to get too hot. Small pans with wide, sloping sides work best. Depending on the size of your pan, you'll need about 1/41/2 cups of batter (60120 mL). Tilt the pan and run the batter along the edges in a circle once or twice. A thin layer should be left along the sides, with a thicker center at the base of the pan. Keep an eye on the hopper. It is ready when the edges are brown and the center is soft but not runny. It may be cooked a minute or two longer if you want the center to be crisp, but many prefer to eat it with a white center. Use a spatula to transfer it to a plate once it's done. Grease the pan between hoppers and check on the hopper frequently during cooking times. Because the pan will heat up as you keep cooking, later hoppers may cook in shorter times. Turn off the heat for a minute or two if the hoppers burn or stick to the pan.
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One-sentence summary -- Start this method the previous day. Cook a handful of rice Soak the uncooked rice in water for at least 4 hours. Drain out the water from the soaked rice. Grind the strained rice, cooked rice, and 3/4 cup (180 mL) grated coconut together. Mix 1/4 cup (60 mL) batter with 3/4 (180 mL) water. Heat the new mixture until thick, then let cool. Mix the cooked and raw batters together. Cover and let sit for 8 hours. Add remaining ingredients to the batter. Dilute the batter until it is easily poured. Grease and heat a pan over medium heat. Use a ladle to add enough batter to coat your pan. Cover with a lid and cook 24 minutes. Cook remaining hoppers the same way.

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 =123456789 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 =147258369 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 =47213986 matrix ZT =43792816 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).
Question: What is a summary of what this article is about?
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.