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Lyrx [107]
3 years ago
6

Suppose that A = PDP-1 . Prove that det(A) = det(D)

Mathematics
1 answer:
daser333 [38]3 years ago
5 0

Answer:

Check.

Step-by-step explanation:

To prove it we need to know that  for two matrices A and B we have that:

det(AB) = det(A)*det(B) and det(A^{-1}) = \frac{1}{det(A)}. Now:

A = PDP^{-1}

det(A) = det(PDP^{-1})

det(A) = det(P)*det(D)*det(P^{-1})

det(A) = det(P)*det(D)*\frac{1}{det(P)}

det(A) = det(P)*\frac{1}{det(P)}*det(D)

det(A) = det(D).

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Maros runs one mile in 7.5 minutes.If he spends a total of 30 minutes running at the same pace, how many miles will he complete?
andrey2020 [161]

Answer:

4 miles

Step-by-step explanation:

30/7.5 = 4

8 0
3 years ago
Read 2 more answers
At the bank of a river, by measurement, a = 9 ft., b = 15 ft., c = 12 ft., and d = 7 ft.How long is x?
Orlov [11]

Answer: x is 20

Step-by-step explanation:

This is ratio

a : c = b : x and d : unknown

a : c = 9 : 12 = 3 : 4 which is 9/12

b : x = 15 : x which is 15 / x

So the proportion will be :

3/4 = 15/x

So Cross multiplying

3x = 90

Divide both side by 3

x = 90/3

x = 20

7 0
3 years ago
9.
elixir [45]
The first one. Hope this helps
Be glad to tell me if it’s correct or not
7 0
3 years ago
Find the sum of 1,503 and 847 and 4,219
iris [78.8K]

1,503 + 847 + 4,219 = 6,569

3 0
3 years ago
The school that Michael goes to is selling tickets to a dance. On the first day of ticket sales the school sold 3 staff tickets
Minchanka [31]

The price of a staff ticket and the price of a student ticket is $8 and $14

Given:

Day 1:

Number of staff tickets sold = 3

Number of students tickets sold = 1

Total revenue day 1 = $38

Day 2:

<em>Number of staff tickets sold</em> = 3

<em>Number of students tickets sold</em> = 2

<em>Total revenue day</em> 2 = $52

let

<em>cost of staff tickets</em> = x

<em>cost of students tickets</em> = y

The equation:

<em>3x + y = 38 (1)</em>

<em>3x + y = 38 (1)3x + 2y = 52 (2)</em>

subtract (1) from (2)

2y - y = 52 - 38

y = 14

substitute y = 14 into (1)

3x + y = 38 (1)

3x + 14 = 38

3x = 38 - 14

3x = 24

x = 24/3

x = 8

Therefore,

cost of staff tickets = x

= $8

cost of students tickets = y

= $14

Read more:

brainly.com/question/22940808

8 0
2 years ago
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