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3 years ago

Prove that if BA=I then BA=AB.

Mathematics

1 answer:

Zanzabum3 years ago

4 0

Answer with Step-by-step explanation:

Since we have given that

$BA=I$

As we know that

AA⁻¹ = I (A is invertible matrix)

Multiplying A⁻¹ on the both the sides:

$BAA^{-1}=IA^{-1}\\\\B=A^{-1}$

Using the above result, we get that

$BA=I=AA^{-1}\\\\BA=AB$

Therefore, BA = AB

Hence, proved.

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Suppose that a college determines the following distribution for X = number of courses taken by a full-time student this semeste

lidiya [134]

Answer:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$ In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$ And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

For this case we have the following distribution given:

X 3 4 5 6

P(X) 0.07 0.4 0.25 0.28

We can calculate the mean with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$

In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$

And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

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3 years ago

What is the area of the parallelogram shown below in square units? 9 units 20 units

tatyana61 [14]

Answer

160

Step-by-step explanation:

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3 years ago

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3 years ago

What is the factored form of 2x2 + x-3?

Vesnalui [34]

Answer:

Step-by-step explanation:

a = 2, b = 1, c = -3

We need to factor this by finding the product of a and c, then from there find which factors of a * c will either add or subtract to give us b.

a * c = 6 and the factors of 6 and 1 and 6, 2 and 3. Well, 6 - 1 doesn't equal 1 and neither does 6 + 1. So our factors are 3 and 2. In order to combine those to get a 1 (our b), we will subtract 2 from 3 since 3 - 2 = 1. That means that 3 is positive and 2 is negative. Filling in the formula with 3 and 2 in place of 1 looks like this (always remember to put the absolute value of the largest number first):

$2x^2+3x-2x-3=0$

Group the first 2 terms together and the second 2 term together in order to factor:

$(2x^2+3x)-(2x-3)=0$ and factor out what's common in each set of parenthesis.

$x(2x+3)-1(2x+3)=0$

Notice that when we factor out a -1 from the second set of parenthesis, we can distribute it back in to get the equation we started with. We know that factoring by grouping "works" if what is inside both sets of parenthesis is exactly the same. Ours are identical: (2x + 3). That is common now, and can be factored out:

$(2x+3)(x-1)=0$

That matches your first choice

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3 years ago

In the first 3 days of class, Maria lost 2 pencils. If maria keeps losing pencils at the same rate for 60 days of class, how man

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Rounded to the nearest whole number, it seems as if she will lose 40 pencils at this rate.

2/3 = .66
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39.6 - 40

Hope this was helpful!

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