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Rudiy27
3 years ago
7

A square matrix A is said to be idempotent iff A2 = A. (i) Show that if A is idempotent, then so is I − A. (ii) Show that if A i

s idempotent, then the matrix 2A − I is also invertible. Hint: Same as before, guess the inverse and check your answer with the definition of inverse.
Mathematics
1 answer:
muminat3 years ago
7 0

Answer:

Step-by-step explanation:

Given that A is a square matrix and A is idempotent

A^2 = A

Consider I-A

i) (I-A)^2 = (I-A).(I-A)\\= I^2 -2A.I+A^2\\= I-2A+A\\=I-A

It follows that I-A is also idempotent

ii) Consider the matrix 2A-I

(2A-I).(2A-I)=\\4A^2-4AI+I^2\\= 4A-4A+I\\=I

So it follows that 2A-I matrix is its own inverse.

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A bird leaves its nest and travels 12 miles per hour downwind for x hours. On the return trip, the bird travels 2 miles per hour
aalyn [17]
12x = 10x + 3

Subtract 10x from both sides

2x = 3
Divide by two on each side

x = 3/2 or 1 1/2 hours



Distance of the trip:

12 * 2 * 3/2 = 36 miles

How long does the trip take:

3/2 + 3/2 + 3/10 = 3 3/10 hours
6 0
3 years ago
Read 2 more answers
The Eagles basketball team scored 12 more than 2 times as many points in the last game of the season than in the first game. Whi
lesya692 [45]

Answer:

A. 12+2p

G. p+p+12

Step-by-step explanation:

The Eagles basketball team scored 12 more than 2 times as many points in the last game of the season than in the first game

Number of points scored in the last game of the season = 2p + 12

A. 12+2p

Equivalent

B. 2+p+12

= P + 14

Not equivalent

C. 2+12p

Not equivalent

D. p(2+12)

= 2p + 12p

Not equivalent

E. p+2+12

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F. 12p+2p

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G. p+p+12

= 2p + 12

Equivalent

3 0
2 years ago
( LETS SEE IF YOUR SMART )
ratelena [41]

Answer:

6\leq x\leq 12

Step-by-step explanation:

First we have to write down what it says in the question in as an expression. So we know that there is already 3 people on Britany's team (herself and the two friends),  that in order to participate in the league you will need at least 9 players, and that the team can have a maximum of 15 player. So....

Let "x" be the number of people who decided to join Britany and her friends

Let "y" be the total number of people on Britanie's team, then .....

3 + x = y

Now we need to remember that in order to participate in the league you will need at least 9 players, and that the team can have a maximum of 15 player. We can write that down as......

9\leq y\leq 15

Now from this we know that the minimum value that x would need to take in order for Brittany's team to participate can be found by solving 3 + x = 9. The maximum value that x would need to take in order for Brittany's team to participate can be found by solving 3 + x = 15. And so we get.....

Minimum value:

3 + x = 9

x = 9 -3

x = 6

Maximum value:

3 + x = 15

x = 15 - 3

x = 12

Now we know that x will be equal to any integer between 6 and 12 so

6\leq x\leq 12

4 0
3 years ago
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g100num [7]
87.5 you multiply the 7 meters by 12.5
7 0
2 years ago
Dividethe product of 45 and25 by the sum of 53 and37
Serhud [2]

Answer:

12.5

Step-by-step explanation:

First you times 45 and 25 together, since product means multilpication. 45*25= 1125

Then you add 53 and 73, which is 90. Then you divide, which equals to the sum of 12.5. Hope this helps!

5 0
3 years ago
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