Problem: Write an article based on this summary: Select a calculator with matrix capabilities. Enter your matrix into the calculator. Select the Edit submenu. Select a name for your matrix. Enter the dimensions of your matrix. Enter each element of the matrix. Quit the Matrix function. Use the inverse key to find the inverse matrix. Convert your inverse matrix to exact answers. Most graphing calculators also have square bracket keys (on TI-84 it's 2nd + x and 2nd + -) which can be used to type in a matrix without using the matrix function.

Answer: Simple 4-function calculators will not be able to help you directly find the inverse. However, due to the repetitive nature of the calculations, an advanced graphing calculator, such as the Texas Instruments TI-83 or TI-86, can greatly reduce the work. First, enter your calculator’s Matrix function by pressing the Matrix key, if you have one. On the Texas Instruments calculators, you may need to press 2nd Matrix. To reach the submenu, you may need to use the arrow buttons or choose the appropriate function key at the top of your calculator’s keypad, depending on the layout of your calculator. Most calculators are equipped to work with anywhere from 3 to 10 matrices, labeled with letters A through J. Typically, just choose [A] to work with. Hit the Enter key after making your selection. This article is focusing on 3x3 matrices. However, the calculator can handle larger sizes. Enter the number of rows, then press Enter, and then the number of columns, and Enter. The calculator screen will show a matrix. If you previously were working with the matrix function, the prior matrix will appear on the screen. The cursor will highlight the first element of the matrix. Type in the value of the matrix you wish to solve, and then Enter. The cursor will move automatically to the next element of the matrix, overwriting any previous numbers.  If you wish to enter a negative number, use your calculator’s negative button (-) and not the minus key. The matrix function will not read the number properly. If necessary, you can use your calculator’s arrow keys to jump around the matrix. After you have entered all values of the matrix, press the Quit key (or 2nd Quit, if necessary). This will exit you from the Matrix function and return you to the main display screen of your calculator. First, reopen the Matrix function and use the Names button to select the matrix label that you used to define your matrix (probably [A]). Then, press your calculator’s inverse key, x−1{\displaystyle x^{-1}}. This may require using the 2nd button, depending on your calculator. Your screen display should show A−1{\displaystyle A^{-1}}. Press Enter, and the inverse matrix should appear on your screen.  Do not use the ^ button on your calculator to try entering A^-1 as separate keystrokes. The calculator will not understand this operation. If you receive an error message when you enter the inverse key, chances are that your original matrix does not have an inverse. You may want to go back and calculate the determinant to find out. The first calculation that the calculator will give you is in decimal form. This is not considered “exact” for most purposes. You should convert the decimal answers to fractional form, as necessary. (If you are very lucky, all your results will be integers, but this is rare.) Your calculator probably has a function that will automatically convert the decimals to fractions. For example, using the TI-86, enter the Math function, then select Misc, and then Frac, and Enter. The decimals will automatically appear as fractions. Note: The calculator will not format the matrix until after the enter/equals key has been used (i.e. everything will be one line and not pretty).


Problem: Write an article based on this summary: Back up your contacts. Save any files you may need. Tap the Settings app on your Android. Tap the Personal tab (if applicable). Tap Backup & reset. Tap Factory data reset. Tap Reset phone. Wait while your device resets. Start the device setup process. Sign in with your Google account when prompted.

Answer: If you are signed in with a Google account on your Android, your contacts should automatically be synced with your Google account. You can check your Google contacts at contacts.google.com. If you have contacts you need to back up manually, see Back Up Your Android Contacts to Your Google Account. When you factory reset, all of your data will be wiped. If you have files on your Android that you need to keep, connect your Android to your computer and transfer the files for safekeeping. See Transfer Data Between a Cell Phone and Computer for detailed instructions. Once your data is safely backed up, you can start the reset process. Some Android devices, notably Samsung devices, will require you to switch to the Personal section to find the reset options.      This will restore your contacts and settings, as well as your Google Play Store app purchases and downloads.


Problem: Write an article based on this summary: Use conductive glass. Make a titanium dioxide solution. Coat the glass. Cook the solar cell. Stain the cells with tea.

Answer:
Most conductive glasses are coated with an indium tin oxide residue. This allows the surface of the glass to conduct electricity rather than insulate it. You can buy conductive glass online or at a solar supply store. This glass is usually found in 1x1in (2.54x2.54 cm) squares. Add ethanol to your titanium dioxide in a glass beaker and stir. You should use the most pure ethanol you can find. Two hundred proof lab grade ethanol is best, but vodka or Everclear will work in a pinch. Use about one milliliter of ethanol per donut and shake or stir the solution in a glass or beaker. Put a layer of tape around three sides of the glass. This will help you control the depth of your coating. Use a dropper or pipet to drop a small amount of the titanium dioxide solution onto the surface of the glass. Use a microscope slide to scrape the the excess liquid off, leaving just a thin coating. Repeat this process ten times. Each drop should be sufficient to coat the glass one time with a thin film. In total, you will use ten drops to form ten layers of titanium dioxide. Put the solar cell into a clear, heatproof beaker or dish. Place the container on a hotplate (or place the solar cell directly on the hotplate). Turn the hotplate on and cook the cell for 10-20 minutes. You will have to watch the cell closely. It will turn brown, and then back to white. When the cell goes back to its original white color, this means that the organic solvents (the ethanol) have burned off, and the cell is finished heating. Teas contain organic compounds known as anthocyanins. These compounds are good at capturing light in the visible spectrum. Brew a cup of herbal tea and submerge the solar cell for a few hours. Darker teas, such as hibiscus, work best. This will stain the cell and allow anthocyanins to bind to the surface of the cell. The cell is now capable of capturing visible light. Prior to staining, the cell could only capture light in the UV spectrum.