![[2013 question paper]](http://s1.studyres.com/store/data/008844912_1-7494f7d6a29d900492173910cd64b54c-300x300.png)
[2013 question paper]
... Part A This section consists of fifteen (15) multiple-choice questions, each with one or more correct answers. Record your answers on the attached bubble-sheet by filling in the appropriate circles. Every question is worth four (4) marks. A solution receives credit if and only if all the correct ans ...
... Part A This section consists of fifteen (15) multiple-choice questions, each with one or more correct answers. Record your answers on the attached bubble-sheet by filling in the appropriate circles. Every question is worth four (4) marks. A solution receives credit if and only if all the correct ans ...
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... A teacher of an algebra III course notices that her students often interpret i in expressions like 3i, i2, and 4i +2 as though it were an unknown or variable, rather than a number. ...
... A teacher of an algebra III course notices that her students often interpret i in expressions like 3i, i2, and 4i +2 as though it were an unknown or variable, rather than a number. ...
THE FUNDAMENTAL THEOREM OF ALGEBRA VIA LINEAR ALGEBRA
... The hypothesis of Lemma 3 is quite restrictive, so Lemma 3 does not apply in too many examples. For instance, it does not apply for any m > 1 when F = Q. We will use Lemma 3 when m is a power of 2. I know no worthwhile applications of Lemma 3 for other values of m. Proof. We induct on the dimension ...
... The hypothesis of Lemma 3 is quite restrictive, so Lemma 3 does not apply in too many examples. For instance, it does not apply for any m > 1 when F = Q. We will use Lemma 3 when m is a power of 2. I know no worthwhile applications of Lemma 3 for other values of m. Proof. We induct on the dimension ...
Evaluating and Simplifying Expressions
... Even if you have never worked with variables, you are probably already familiar with combining like terms. For example, the sum of 4 boxes and 5 boxes is 9 boxes. You simply add (4 + 5 = 9) and keep the “boxes” as the like units. Now let x be a variable that represents one box. The calculation becom ...
... Even if you have never worked with variables, you are probably already familiar with combining like terms. For example, the sum of 4 boxes and 5 boxes is 9 boxes. You simply add (4 + 5 = 9) and keep the “boxes” as the like units. Now let x be a variable that represents one box. The calculation becom ...
1 Vector Spaces
... Remark 1. If X has a basis of n vectors e1 , . . . , en , then these basis vectors are linearly independent. This is because O = 0e1 + · · · + 0en uniquely. The next two theorems follow immediately from the previous discussion. Theorem 1. If dim X = n and e1 , . . . , en are linearly independent vec ...
... Remark 1. If X has a basis of n vectors e1 , . . . , en , then these basis vectors are linearly independent. This is because O = 0e1 + · · · + 0en uniquely. The next two theorems follow immediately from the previous discussion. Theorem 1. If dim X = n and e1 , . . . , en are linearly independent vec ...
