When solving -1/5(x-25) = 7, what is the correct sequence of operations?

The 3 × 3 matrix P satisfies the matrix equation P^2 = P.

riadik2000 [5.3K]

Answer: The answers are given below.

Step-by-step explanation: Given that a 3 × 3 matrix P satisfies the matrix equation P² = P.

We are to

(a) find the possibilities for the determinant of P.

(b) explain the reason behind there are no other possibilities.

(c) give an example of P, for each possible determinant.

(a) According to the given information, we have

$P^2=P\\\\\Rightarrow P^2-P=0\\\\\Rightarrow P(P-I)=0\\\\\Rightarrow P=0,~~~P=I.$

So, P can be either a zero matrix of order 3 or an identity matrix of order 3.

If P = 0, then det(P) = 0 and if P = I, then det(P) = 1.

Therefore the possible determinants of P are 0 and 1.

(b) There can be any other determinant other than 0 and 1, because if so, then the given equation P² = P will not be satisfied.

(c) If |P| = 0, then the matrix P can be can be of the form as follows:

$P=\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right] .$

If |P| = 1, the the matrix P can be of the form as follows :

$P=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] .$

Thus, all the parts are answered.

4 0

2 years ago

Rachel rides her bike due east at 9 miles per hour. Amos rides his bicycle due north at 12 miles per hour. If they left from the

Svetach [21]

They will be 15 miles apart after one hour if they left the same point at the same time.

<h3>How do we measure and calculate the distance in Geometry?</h3>

The distance between two points in geometry can be calculated by using the Pythagoras theorem.

Mathematically, the Pythagoras theorem can be expressed as:

$\mathbf{d = \sqrt{x^2 +y^2}}$

where;

x and y are opposite and adjacent sides respectively.

$\mathbf{d = \sqrt{(9)^2 +(12)^2}}$

$\mathbf{d = \sqrt{81+144}}$

$\mathbf{d = \sqrt{225}}$

d = 15 miles

Therefore, we can conclude that they will be 15 miles apart after one hour if they left the same point at the same time.

Learn more about calculating the distance between two points here:

brainly.com/question/7243416

#SPJ1

5 0

1 year ago

Please help me! i’m really confused on this because i keep getting -5 outside the thing

Leona [35]

Answer: D.

Step-by-step explanation: First you find the common factor, which is 5x³y. Then you write in parenthesis what's left over from each term. So the answer should look like: 5x³y(-3x⁵-4z+9).

4 0

1 year ago

X^3 times x^? equals to x^17 <br><br> what’s the missing exponent?

ElenaW [278]

Answer:

14

Step-by-step explanation:

The applicable rule of exponents is ...

(a^b)(a^c) = a^(b+c)

__

You have ...

(x^3)(x^a) = x^17

x^(3+a) = x^17

Equating exponents, we get ...

3 +a = 17

a = 14

The missing exponent is 14.

5 0

3 years ago

Can you please help me?

yan [13]

Answer:

-3, -4, -4, 0, 16, 64, 192.

Step-by-step explanation:

I don't know for sure if this is correct, but when i did it theses are the answers i got. You do y=8*2^x. Meaning you substitute the x for the x values such as -3, -2, and -1.

Also if you have one there's a setting you can go to on an actual calculator and type in this on a Y/X chart. I didn't use one this time because i don't have one, but thought you'd find that information useful.

6 0

2 years ago