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Commutative Property Of Addition 2. If A is an n×m matrix and O is a m×k zero-matrix, then we have: AO = O Note that AO is the n×k zero-matrix. Matrix Matrix Multiplication 11:09. We have 1. To understand the properties of transpose matrix, we will take two matrices A and B which have equal order. The identity matrix i... | [
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... | 4,479 |
# Comparing the magnitudes of expressions of surds
I recently tackled some questions on maths-challenge / maths-aptitude papers where the task was to order various expressions made up of surds (without a calculator, obviously).
I found myself wondering whether I was relying too much on knowing the numerical value of ... | [
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1973,
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315,
1729,
5356,
320,
... | 1,385 |
# In Calculus, how can a function have several different, yet equal, derivatives?
I've been pondering this question all night as I work through some problems, and after a very thorough search, I haven't found anything completely related to my question. I guess i'm also curious how some derivatives are simplified as we... | [
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11,
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264,
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17423,
2711,
11,
358,
8990,
... | 1,546 |
# Math Help - working backwards - cubics
1. ## working backwards - cubics
Write an equation that has the following roots: 2, -1, 5
Answer key: x^3 - 6x^2 + 3x + 10 = 0
For quadratic equations, I use the sum and product of roots, this is a cubic equation, how do I solve this?
Thanks.
2. Originally Posted by shento... | [
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11,
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20,
271,
16141,
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25,
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61,
18,
481... | 1,704 |
# Work and time, when work is split into parts
I'm stuck on a particular type of work and time problems.
For example,
1) A,B,C can complete a work separately in 24,36 and 48 days. They started working together but C left after 4 days of start and A left 3 days before completion of the work. In how many days will the... | [
2,
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220,
17,
19,
11,
18,
2... | 2,315 |
# Algebraic Manipulation
## Definition
Algebraic manipulation involves rearranging variables to make an algebraic expression better suit your needs. During this rearrangement, the value of the expression does not change.
## Technique
Algebraic expressions aren't always given in their most convenient forms. This is ... | [
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Inequality involving sums with binomial coefficient
I am trying to show upper- and lower-bounds on
$$\frac{1}{2^n}\sum_{i=0}^n\binom{n}{i}\min(i, n-i)$$
(where $$n\geq 1$$) in order to show that it basically grows as $$\Theta(n)$$.
The upper-bound is easy to get since $$\min(i, n-i)\leq i$$ for $$i\in\{0, \dots n\}... | [
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913... | 3,385 |
The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal to the number of rows of the 2nd one. The dimensions of $B$ are $3\times 2$ and the dimensions of $A$ are $2\times 3$. The dot product involves multiplying the corresponding elements in the row of the first matrix, by... | [
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... | 5,723 |
"# Definite Integral: $\\int_0^1\\frac{\\ln^4(x)}{x^2+1}\\,dx$\n\nI'm trying to derive a closed-form(...TRUNCATED) | [2,3892,15856,91660,25,57960,396,62,15,61,16,59,37018,35702,2261,61,19,2075,9139,90,87,61,17,10,16,1(...TRUNCATED) | 6,336 |
"# Divisibility Rule for 9\n\nI'm working through an elementary number theory course right now and I(...TRUNCATED) | [2,8765,285,3147,18100,369,220,24,271,40,2776,3238,1526,458,35156,1372,10126,3308,1290,1431,323,358,(...TRUNCATED) | 1,385 |
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