Write an article based on this "Check the determinant of the matrix. Transpose the original matrix. Find the determinant of each of the 2x2 minor matrices. Create the matrix of cofactors. Divide each term of the adjugate matrix by the determinant."
article: You need to calculate the determinant of the matrix as an initial step. If the determinant is 0, then your work is finished, because the matrix has no inverse. The determinant of matrix M can be represented symbolically as det(M). For a 3x3 matrix, find the determinant by first To review finding the determinant of a matrix, see Find the Determinant of a 3X3 Matrix. Transposing means reflecting the matrix about the main diagonal, or equivalently, swapping the (i,j)th element and the (j,i)th. When you transpose the terms of the matrix, you should see that the main diagonal (from upper left to lower right) is unchanged. Another way to think of transposing is that you rewrite the first row as the first column, the middle row becomes the middle column, and the third row becomes the third column. Notice the colored elements in the diagram above and see where the numbers have changed position. Every item of the newly transposed 3x3 matrix is associated with a corresponding 2x2 "minor" matrix. To find the right minor matrix for each term, first highlight the row and column of the term you begin with. This should include five terms of the matrix. The remaining four terms make up the minor matrix. In the example shown above, if you want the minor matrix of the term in the second row, first column, you highlight the five terms that are in the second row and the first column. The remaining four terms are the corresponding minor matrix. Find the determinant of each minor matrix by cross-multiplying the diagonals and subtracting, as shown. For more on minor matrices and their uses, see Understand the Basics of Matrices. Place the results of the previous step into a new matrix of cofactors by aligning each minor matrix determinant with the corresponding position in the original matrix. Thus, the determinant that you calculated from item (1,1) of the original matrix goes in position (1,1). You must then reverse the sign of alternating terms of this new matrix, following the "checkerboard" pattern shown. When assigning signs, the first element of the first row keeps its original sign. The second element is reversed. The third element keeps its original sign. Continue on with the rest of the matrix in this fashion. Note that the (+) or (-) signs in the checkerboard diagram do not suggest that the final term should be positive or negative. They are indicators of keeping (+) or reversing (-) whatever sign the number originally had. For a review of cofactors, see Understand the Basics of Matrices. The final result of this step is called the adjugate matrix of the original. This is sometimes referred to as the adjoint matrix. The adjugate matrix is noted as Adj(M). Recall the determinant of M that you calculated in the first step (to check that the inverse was possible). You now divide every term of the matrix by that value. Place the result of each calculation into the spot of the original term. The result is the inverse of the original matrix. For the sample matrix shown in the diagram, the determinant is 1. Therefore, dividing every term of the adjugate matrix results in the adjugate matrix itself. (You won't always be so lucky.) Instead of dividing, some sources represent this step as multiplying each term of M by 1/det(M). Mathematically, these are equivalent.

Write an article based on this "Monitor your hair until it has turned pale blonde. Rinse the bleach out of your hair. Shampoo and condition your hair. Dry your hair by wrapping it in a towel."
article: Check your hair every couple of minutes using a mirror to watch the lightening process. Your hair will experience several color changes, going from orange to yellow to pale blonde when you have dark brown hair. Bleach normally takes at least 30 minutes to work, but it will likely take more than 1 session to go from black to blonde. Bleaching black hair to pale blonde will take a lot longer than other hair colors. The amount of time that it takes for your hair to reach pale blonde will depend on your original hair color, and the type of bleach that you are using. The instructions for the bleach kit will give you an accurate length of time that the process will take. Once your hair has reached pale blonde, thoroughly rinse the bleach out straight away. Cold or lukewarm water works best. Make sure that the water is still cold or lukewarm, and wash your hair with shampoo and then conditioner. Natural or baby shampoos and conditioners are ideal because they are very gentle on your hair, which is necessary after bleaching. Shampoo and conditioner which is natural and specifically designed to hydrate and moisturise your hair are also good choices. Cold or lukewarm water is best because it closes the pores and leaves your hair shiny when it's dry. Bleach weakens your hair, so this will help to keep it protected while it's drying. Never rub your hair with the towel, as this could weaken it further. Don't comb your bleached hair until it is fully dry.

Write an article based on this "Know what a healthy weight is for your body type. Figure out how many calories you need to eat and burn. Understand and track calorie intake. Plan to keep a log. Get support. Consult a physician."
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To determine what your healthy goal weight should be, use the body mass index (BMI), which can be used to predict risk for chronic diseases. BMI is a person's weight in kilograms (kg) divided by the square of the person's height in meters (m). Identify the weight you would like to be in kilograms and then divide that by your height in meters to see if it is healthy. You can also use a BMI calculator, such as the one on the NIH's website: https://www.nhlbi.nih.gov/health/educational/lose_wt/BMI/bmicalc.htm Increase or decrease that goal weight so that it fits within the BMI range considered healthy: A BMI below 18.5 is considered underweight. A BMI of 18.5-24.9 is a normal or healthy weight. A BMI of 25-29.9 is considered overweight, while a BMI greater than 30 is considered obese. Along with finding a healthy weight, also realize what is realistic. If you are 100 lb away from your healthy body weight with only a month before summer, consider setting a smaller, more attainable goal. The more calories you cut back, the more weight you will lose; however, it is important that you do not eat less than your Basal Metabolic Rate, the amount of calories your body needs to function effectively when at rest. This number can be calculated using an online BMR calculator. In general, don't aim to lose more than one to two pounds per week. A loss of one to two pounds per week is a healthy rate at which to lose weight; any more than this could be too drastic a change and may signify that your body is not getting what it needs. To do this, try to eat 250 fewer calories per day and burn an extra 250 calories a day. This ratio will create enough of a calorie deficit that you should lose one pound per week. During the summertime, you are surrounded by opportunities to eat, whether it's at a barbecue, pool party, ice cream party, or summer luau. However, if you want to lose weight over the summer, it's important that you cut back on the number of calories you eat. As a general rule, weight loss occurs when you burn more calories than you consume. To help figure out how many calories you normally eat each day, track your food for a day by writing down the number of calories in everything you eat and drink. Calories are listed on the back of food labels. For foods that do not have labels, you can find information about the caloric value of certain foods online through the USDA Food Database. Pay attention to the number of servings you eat and multiply this by the number of calories per serving. For example, if you ate 30 chips and a serving size is 15 chips, you need to multiply the number of calories by two since you ate two servings. Once you have figured out how many calories you normally eat, cut down this number by 500-1000 calories per day to lose weight. In this log, record what you eat and the type and duration of exercise you're doing every day. This is a simple yet very powerful tool to keep yourself accountable. The log will help you track your progress and see whether you are keeping to your healthy diet and exercise regimen. This is a wonderful way to hold yourself accountable and stay on track. There are many apps for smart phones that have capabilities to track food intake, energy expenditure, water intake and more! Often, we tend to overlook the snacking we do between meals and instead think our diet is not working. Studies have shown that most people underestimate how much they eat by 25 percent. In addition, many of us think we get more exercise and burn more calories than we do. Use the log to identify how many calories your exercisewhether it be a run on the treadmill or a spin on the bikeis burning. If you use cardio machines at a gym, the number of calories is usually digitally calculated and displayed. Make sure to put in your particulars, such as weight and age, to achieve an accurate count. There are also online charts that can help tell you how many calories a half hour or an hour of a given exercise burns. You might also discover useful information about your daily habits and a reality check about how many calories you actually consume and burn off through exercise. Once you know your habits and patterns better, you can begin to address problem behaviors that are hindering your progress. Find a partnerwhether that be a spouse, friend, or family memberwho wants to join you during outdoor activities, hit the gym with you, or join your healthy eating plan. Having social support will make it easier to lose weight because the other person will also keep you accountable and be a sounding board for any obstacles and struggles you face along the way. If you cannot find a friend or partner to help you with your weight loss journey, utilizing the services of a personal trainer or registered dietitian will keep you accountable and help you stay active and eat healthy. A trainer can also be a huge support system. Think outside of the box for your support system! Always consult your physician before beginning any type of weight loss and/or exercise program. You should also consult your physician throughout your weight loss program and keep him updated of any changes or symptoms you may be experiencing, such as constipation thanks to your new diet plan or lethargy due to not getting enough food. In addition, you should also talk to your doctor if you are eating well, tracking your calories and watching what you eat, exercising, and are still not losing weight. This could be indicative of a more serious underlying medical condition, such as a thyroid problem.