Problem: Article: Linear equations have distinct components. The variable is the symbol (usually a letter like x or y) for a number you do not yet know. The constant is a number that remains consistent. The coefficient is a number before a variable, which is used to multiply it. For example, in the linear equation 2x + 4y = 8, x and y are variables. The constant is 8. The numbers 2 and 4 are coefficients. A system of equations with two variables can be written as follows:ax + by = pcx + dy = qAny of the constants (p, q) can be zero, with the exception that each equation must have at least one variable (x, y) in it. When you have a linear system, you can use a matrix to rewrite it, then use the algebraic properties of that matrix to solve it. To rewrite a linear system, you use A to represent the coefficients matrix, C to represent the constants matrix, and X to represent the unknown matrix. The linear system above, for example, can be rewritten as a matrix equation as follows: A x X = C. An augmented matrix is a matrix obtained by appending columns of two matrices. If you have two matrices, A and C, which looks like this:You can create an augmented matrix by putting them together. The augmented matrix would look like this: For example, consider the following linear system:2x + 4y = 8x + y = 2Your augmented matrix would be a 2x3 matrix that looks like this:
Summary: Know your terminology. Recognize the form for a system of equations. Understand matrix equations. Understand augmented matrices.

INPUT ARTICLE: Article: A sheepskin rug can be brought back to life with a non-alkaline, pH balanced cleanser, like baby shampoo or sheepskin wash. Fill a bathtub with warm water and 14 cup (59mL) mild cleanser. Lightly agitate the sheepskin in the water for 5 minutes and roll it up to squeeze out the water. Put it in your washing machine on the spin cycle to further remove excess water and lay it out to dry for the day. Lay the sheepskin out to dry away from direct sunlight. Use a metal brush to comb out the wool after it dries. To eliminate odors and freshen up fur and sheepskin rugs sans water, sprinkle unscented talcum powder or baking soda on your rug. Leave the powder on for a few hours, shake and brush out, and repeat as needed. If your rug is small enough to put in the washing machine and the care instructions do not advise against it, throw it in there. Adjust the washing machine cycle to gentle first, place the rug in a pillowcase or mesh bag and tumble dry on low. Don't put a rug with a rubber backing in the washing machine. If the rubber begins to degrade and flake off, it could clog up your washing machine. If you have a true, high-pile shag carpet, using a vacuum cleaner may be risky business. The rug fibers may get caught in the vacuum and become frayed. Turn your vacuum setting to high-pile or shake out dirt from a shag rug.

SUMMARY: Wash sheepskin with baby shampoo. Freshen up fur and sheepskin with talcum powder or baking soda. Clean woven rugs in the washing machine. Be careful vacuuming a shag carpet.

In one sentence, describe what the following article is about: What are these principles and why are they important? For most people, aggressive violence falls into this category, as does stealing and lying. But this self-examination of morals is perhaps the most important step to determine moral principles without religion. It is okay, even expected, not to have full answers for every question, but you should ask them:[[Image:Determine Moral Principles Without Religion Step 4 Version 2.jpg|center] Is it ever right to commit a crime? Is it right to follow all laws or only those you agree with? Is total honesty a good thing, or is it unattainable? What is your line between helping your group or community and looking out for yourself? Who or what are you loyal to? Do you ascribe to similar moral principles? Morality should not say how we live in this life in order to obtain a better position in the possible afterlife. Instead, morality should maximize utility in this life, because there are very real issues and ideas on Earth that need your thoughtful care. One can concoct a moral code with many different goals and aims, but it remains that this life is the only one we have. This principle should never be far from your mind. Your actions have consequences in the real world, for your life and the lives of others. Don't ignore these effects in an effort to plan for the afterlife-- make the most of your present situation. Religions (generally) believe that evil or bad actions are the failure of the individual. It is someone's fault, as they strayed from the moral tenants of religion out of selfishness, anger, or some internal evil or flaw. But most evil acts are the result not of consciously evil people, but rather the circumstances surrounding them. For example: Rape and male violence can, in some circumstances, propagate the human race, as "evil" men like Genghis Khan created hundreds of offspring in their evolutionary (and sub-conscience) desire to spread his DNA. These violent tendencies still run in modern-day humans, as it was a highly "successful" genetic mutation to rape and pillage in ancient times. Frequently, evil is done in an effort to survive, even if that effort is fundamentally misguided. While Hitler's actions are unquestionably immoral, what about the rest of the Germans that went along with it? The entire country was in horrible poverty and depression, and a charismatic leader convinced them he could return them to safety and wealth -- the choice wasn't considered moral, it was practical. This is a continuing task and one's moral principles must be updated as society progresses and new ideas and situations are discovered. One of the big mistakes in religious morality is that people assume that everything has been right for 2,000 or more years and that no changes need to be made to fit modern times. But this often betrays the underlying moral tenants of treating others fairly and avoiding violence, as modern-day sects of Islam can attest. Keep your mind more open than this and secular moral principles will soon become much clearer. Everyone should spend time re-thinking their moral code to fit new problems and issues. Look no further than Pope Francis, who quickly set about reexamining and modifying centuries-old Catholic dogma about homosexuality, women, the environment, and capitalism. Think about your morals and follow them, whatever they may be. It doesn't make sense to have a set of moral principles which one does not abide by. Remember that other people have different ideas of morals, and accept that you can do no more than to follow your own code. Ultimately, your morality is going to be determined by your actions and words, not by your thoughts.
Summary:
Consider the most certain principles of your life, the principles that you never violate. Understand that this life is the only one we have. Consider the real-world causes and inspirations of amoral behavior. Continue reevaluating and adjusting your morals to be both up-to-date and consistent. Illustrate your moral code in actions, not just in thoughts.