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3 years ago

When is x - y = 4x - 4y

Mathematics

1 answer:

Setler79 [48]3 years ago

3 0

The answer is
When x = 4
Y = 4
Maybe the answer is correct

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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

3 years ago

Tom has 7/8 gallons of paint. He used 1/2 gallon of paint on a project. He uses the steps to show how much paint he had when he

WINSTONCH [101]

He made his mistake in Step 2. Tom should have subtracted 4/8 instead of 1/8. The mistake is that he was not consistent when he multiplied Denominators (bottom number) must be the same when handling fractions so Tom must multiply both the numerator and denominator by the SAME number to balance it out. 1/2 x 4/4= 4/8. Subtract. 7/8 - 4/8= 3/8. Tom has 3/8 of a gallon of paint leftover.

4 0

3 years ago

Read 2 more answers

An event lasts 4 hours and 20 minutes. How long did the event last in seconds?

enyata [817]

20*6=120seconds +3600second in an hour so 3600*4=14400

1210+14400=14520

14520 is the answer I hope this helps!

8 0

3 years ago

Read 2 more answers

Which methods could you use to calculate the y-coordinate of the midpoint of vertical line segment with endpoints at (0,0) and (

Hatshy [7]

Answer:

Midpoint formula.

The midpoint formula is (x_1+x_2)/2 , (y_1+y_2)/2

Step-by-step explanation:

This is one method. A list wasn't provided.

5 0

3 years ago

Function help please

Korvikt [17]

Answer:

The first table represents a function.

Step-by-step explanation:

For it to be a function, there needs to be 1 unique y value of 1 unique x value.

Looking at 2nd table, we see x value of -5 is mapped to 2 different y values of -5 and 5. So this is not a function.
Looking at 3rd table, we see x value of -2 is mapped to 2 different y values of 2 and 4. So this is not a function.
Looking at 4th table, we see x value of -4 is mapped to 2 different y values of 2 and 0. So this is not a function as well.

Looking at table 1, there are no duplicate x values and each of the 4 x values map to different values. So the first table represents a function.

4 0

3 years ago