Graph is shown in the figure. y 2 y= 20 (2, 10) (0,5) х

Prove that A is idempotent if and only if AT is idempotent. Getting Started: The phrase "if and only if" means that you have to

Otrada [13]

Answer:

It is proved that A is idempotent if and only if $A^T$ is idempotent.

Step-by-step explanation:

Case-1 : First assume that A is idempotent that is, $A^2=A$ . We have to show by using this $(A^T)^2=A^T$ . So,

$(A^T)^2=A^T\times A^T=(A\times A)^T=(A^2)^T=A^T$

Thus $A^T$ is idempotent.

Case-2 :

Conversly, assuming $A^T$ is idempotent, thet is, $(A^T)^2=A^T$ . We have to show $A^2=A$ . So,

$A^2=A\times A=(A^T)^T\times(A^T)^T=(A^T\times A^T)^T$

$=((A^T)^2)^T=(A^T)^T=A$

Thus A is idempotent. Hence proved.

3 0

3 years ago

What is the slope of the line shown below?

marta [7]

Answer:

i think is A

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Based on a sample of 150 textbooks at the store, you find an average of 70.69 and a standard deviation of 29.6. The point estima

Ugo [173]

Answer:

Step-by-step explanation:

Given that:

The sample size = 150

The sample mean = 70.69

The standard deviation = 29.60

The sample mean is equal to the point estimate of the population = 70.69

At 99% confidence interval level is:

∝ = 1 - 0.99

∝ = 0.01

The critical value:

$Z_{\alpha/2} = Z_{0.01/2} \\ \\ Z_{0.005} = 2.58 \ using \ Z \ tables$

The Margin of error = $Z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}$

$= 2.58 \times \dfrac{29.6}{\sqrt{150}}$

= 2.58 × 2.4168

≅ 6.235

At 99% confidence interval; the estimate of the population mean lies within the interval:

= $\overline x - E < \mu \ < \overline x + E$

= 70.69 - 6.235 < μ < 70.69 + 6.235

= 64.455 < μ < 76.925

= (64.455 , 76.925 )

6 0

3 years ago

ASAP please help me

lesya692 [45]

So his lawn can be divided into 4 shapes: 1 rectangle, 2 triangles, and an irregular shape. So you get the area of the rectangle which is 48*120=5,760.

For the part above the rectangle, you can see that the 2 triangles and the irregular shape make one large triangle so take the area of that. (I’m going to refer to this as the BIG triangle).
.5*40*120=2,400
The base of the triangle is equal to the base of the rectangle. The height of the triangle you get by subtracting the height of the WHOLE lawn by the height of the rectangle. (88-48=40).

Inside that large triangle made up of three shapes, you can see another triangle that’s made up of one triangle and the irregular shape. I’ll refer to this triangle as triangle 1.
Take the area of that triangle.
.5*25*75=937.5
The base of the triangle you get by adding the base of the smaller triangle and the irregular shape. (51+24=75)

Inside the triangle you just took the area of (triangle 1) is another triangle (which I’ll refer to as triangle 2). Take the area of triangle 2.
.5*51*17=433.5

Subtract the area of triangle 1 by the area of triangle 2 and that’ll give you the area of the irregular shape.
937.5-433.5=504

So now you add the areas of the BIG triangle and the rectangle.
5760+2,400=8160
Make sure you subtract the irregular shape since it isn’t part of the lawn’s area.
8160-504=7656

So the lawn is 7656 square feet. Multiply it by .005. That equals 38.28. That’s how much fertilizer he needs to use.

Multiply 1.25 to 38.28 to get the amount of money he needs to spend.

47.85 dollars

I might’ve made a few mistakes but I hope my reasoning was at least understandable

7 0

3 years ago

Read 2 more answers

I need to find the surface of the figure

ikadub [295]

360!!!!!!!!!!!!!!!!!!!!

3 0

3 years ago

Read 2 more answers