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Lyrx [107]
4 years ago
6

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

Mathematics
1 answer:
daser333 [38]4 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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A bicycle helmet has a selling price of $50. The helmet is discounted 30% off the selling price. The sales tax rate is 6%. What
Andrei [34K]
Convert 30% to a decimal by dividing by 100 = 0.30

Multiply by the cost of the helmet, $50
50 x 0.30 = $15, the amount of the discount.

50-15 = $35, the sale price of the helmet.

For the sales tax, again, convert to a decimal by dividing by 100 = 0.06

35 x 0.06 = 2.10, the amount of sales tax

$35 + $2.10 = $37.10, total cost with tax
6 0
3 years ago
Bobs supermarket sells red apples and green apples at the ratio of 5:3.
nika2105 [10]

Answer:

10 red apples and 6 green apples

Step-by-step explanation:

first you multiply 5×2 to get 10 apples

then you multiply 3×2 to get 6 apples

5 0
3 years ago
Marie has 8 hours to write a 45 page chatper for her book Marie writes at a constant speed of 4 pages per hour will Marie comple
zubka84 [21]

Answer:

She wont complete the book in book in time at 4 pages per hour has she will only write 32 pages in 8 hours

Step-by-step explanation:

Marie has 8 hours to write 45 page chapter

at 4 page per hours, in 8 hours, she will on write

8 × 4 = 32 pages

Therefore, she wont complete it in time at 4 pages per hour

5 0
3 years ago
Two ratios by entering less than greater than or equal than 16 to 15, 30 to 80
Mumz [18]

Answer:

6:15>30:80

Step-by-step explanation:

The ratio;

6:15 written in the form x/1 is equivalent to 2/5 or 0.4

30:80 written in the form x/1 is equal to 3/8 or 0.375

0.4 is greater than 0.375

Therefore;

<u>6:15>30:80</u>

6 0
3 years ago
Find the lateral surface area of the figure.
Brut [27]

Surface area of the cylinder = 816.4 sq. ft.

Solution:

Height of the cylinder = 21 ft

Diameter of the cylinder = 10 ft

Radius of the cylinder = 10 ÷ 2 = 5 ft

Use the value of \pi = 3.14

Surface area of the cylinder = 2 \pi r h+2 \pi r^{2}

Substitute the given values in the surface area formula, we get

Surface area of the cylinder $=2\times3.14\times 5\times 21+2 \times3.14\times 5^2

                                               =659.4+157

                                               =816.4 ft²

Hence the surface area of the cylinder is 816.4 sq. ft.

7 0
3 years ago
Read 2 more answers
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