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Chapter 1.1

Mat223 Chapter 1.1

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Sean Uppal

The Linear Equation in eample 2 is inconsisten because no Sn was found. Example 3: Solution: This time we can multiply the first equation by 3/2. This time we have 0 = 0. Which means the relationship between x1 and x2 are the same in both equations. This is isolating x1 on one side in the above equation. (I don’t get above equation) S1 in the case is the free variable. This is known as the general solution because it gives all the solution to the system of equations. The graph only shows one line because they are two equations with identical lines. The two lines have an infinitely amount of points intersecting. When you connect 2 cardboard, like the above image, you will realize that the above image will create planes. The equations with 3 variables are no longer lines they are planes. And therefore because they are planes, you will discover that the answers are either 0 or inconsistent. Meaning that the lines either intersect infinitely or they don’t at all. This is what it looks like if it were 3 planes instead of one. As you can see there are solutions to inconsistent, infinitely intersections, unique points and (b) – don’t get what that is. Example 4: The method that we will use is called back substitution.
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