All categories

3 years ago

(20 POINTS AND BRAINLIEST FOR BEST)

Mathematics

1 answer:

Lena [83]3 years ago

7 0

Answer:

i used be so good at this now i suck because it's been awhile

Step-by-step explanation:

You might be interested in

Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .

neonofarm [45]

Let $\mathbf A$ be a rectangular $m\times n$ matrix with column vectors $\mathbf a_1,\ldots,\mathbf a_n$ , i.e.

$\mathbf A=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}$

Then we have

$\mathbf A^\top=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}^\top$

and the product of the two is

$\mathbf A^\top\mathbf A=\begin{bmatrix}\mathbf a_1\cdot\mathbf a_1&\mathbf a_1\cdot\mathbf a_2&\cdots&\mathbf a_1\cdot\mathbf a_n\\\mathbf a_2\cdot\mathbf a_1&\mathbf a_2\cdot\mathbf a_2&\cdots&\mathbf a_2\cdot\mathbf a_n\\\vdots&\vdots&\ddots&\vdots\\\mathbf a_n\cdot\mathbf a_1&\mathbf a_n\cdot\mathbf a_2&\cdots&\mathbf a_n\cdot\mathbf a_n\end{bmatrix}$

Because the columns of $\mathbf A$ are orthonormal, we have

$\mathbf a_i\cdot\mathbf a_j=\begin{cases}1&\text{for }i=j\\0&\text{for }i\neq j\end{cases}$

which means $\mathbf A^\top\mathbf A$ reduces to an $n\times n$ matrix with ones along the diagonal and zero everywhere else, i.e.

$\mathbf A^\top\mathbf A=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}=\mathbf I_n$

where $\mathbf I$ denotes the identity matrix. This means the solution to $\mathbf{Ax}=\mathbf b$ is given by

$\mathbf A^\top(\mathbf{Ax})=\mathbf A^\top\mathbf b\implies(\underbrace{\mathbf A^\top\mathbf A}_{\mathbf I})\mathbf x=\mathbf A^\top\mathbf b\implies\mathbf x=\mathbf A^\top\mathbf b$

6 0

3 years ago

A large sample of tires from cabs driven within a city have an average tire tread depth of 0.25cm at the end of the winter. If t

frutty [35]

Answer:

0% probability cab tires depths would be shallower than 0.25cm.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 2.2, \sigma = 0.33$

What is the probability cab tires depths would be shallower than 0.25cm.

This probability is the pvalue of Z when X = 0.25. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.25 - 2.2}{0.33}$

$Z = -5.9$

$Z = -5.9$ has a pvalue of 0.

0% probability cab tires depths would be shallower than 0.25cm.

7 0

3 years ago

Helpppppppppppppppppppp

alisha [4.7K]

Answer:

6:5:4

Step-by-step explanation:

6 + 5 + 4 = 15

3000/15 = 200

200 x 6 = 1200 = eldest

200 x 5 = 1000 = 2nd eldest

1200 + 1000 = 2200

3000 - 2200 = 800

200 x 4 = 800 = youngest

6 0

3 years ago

Read 2 more answers

Which of the following is the complete factorization of 25a 2-100

Westkost [7]

Answer:

25(a-2)(a+2)

Step-by-step explanation:

25a^2 -100

We can factor out 25

25(a^2 -4)

a^2 -4 is the difference of squares a^2-b^2= (a-b)(a+b)

where a =a and b=2

a^2 -4 = (a-2)(a+2)

25a^2 -100 = 25(a-2)(a+2)

4 0

3 years ago

R=2/3t +v...solve for t...thanks

mote1985 [20]

$\dfrac{2}{3}t+v=r\ \ \ |subtract\ v\ from\ both\ sides\\\\\dfrac{2}{3}t=r-v\ \ \ \ |multiply\ both\ sides\ by\ \dfrac{3}{2}\\\\\boxed{t=\frac{3}{2}(r-v)}$

4 0

3 years ago

Read 2 more answers