15 points if you can asnwer puh-lease

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .

5 0

4 years ago

Pls answer this question for ill give brainliest

notka56 [123]

Answer:

BE=15

Step-by-step explanation:

Since E is the center, BE=2x+1

And AC is 6x-12 with E being a midpoint.

Since AC is 2 segments and BE is only 1 then you multiply 2x+1 by 2 so that

you can find x. You multiply 2x+12 by 2 because E is the midpoint so that means ED is the same value as BE

6x-12=4x+2

BD=AC

6x-4x-12=2

2x=2+12

2x=14

x=7

BE= 2x+1

2(7)=14+1=15

7 0

3 years ago

Toni bought 5 t-shirts for 35 if each T-shirt cost the same amount .how much tony would pay for20 shirts

Sergeeva-Olga [200]

Answer: The answer is Toni can buy 20 tee shirts for 140 dollars

Step-by-step explanation:

First you find out how many times 5 can go into 20

Next you see that 5 can go into 20, 4 times so you take the 35 and multiply 4 and you get 140 so you can buy 20 tee shirts for 140 dollars.

8 0

3 years ago

For A brainlist ** explain

IrinaVladis [17]

Answer:

So interval notation is with ( and [ where ( is exclusive and [ is inclusive.

Like (1,2) is between 1 and 2 exclusive. [1,2] is between 1 and 2 inclusive. (1,2] is between 1 and 2, 1 exclusive 2 inclusive.

at the point (6,0) you see that the graph goes from above 0 to below 0 (from positive to negative)

The values are positive when x is less than 6 and negative when x is greater than 6.

so the positive interval is

(-infinity, 6)

and with inifinity you always use exclusive

It's that because everything from all the way to the left (-infinity) to 6, is above the x-axis, which means it's positive

using this logic can you do the negative interval?

5 0

3 years ago

Special segments in circles

pochemuha

If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.
I'm assuming that number up top is an 8. It's kind of blurry.

Since ten is a chord, and x is a segment of it, it can be expressed as x and 10 - x.
3(8) = x(10 - x)
$24 = 10x - x^{2}$
$x^{2} - 10x + 24 = 0$
(x - 6)(x - 4) = 0
x - 6 = 0 .... x - 4 = 0
x = 6 .... x = 4

4 or 6

4 0

3 years ago

15 points if you can asnwer puh-lease​

15 points if you can asnwer puh-lease