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Aleksandr-060686 [28]
2 years ago
7

The dimension of the row space of a 3 x 5 matrix A is 2 d. What is the dimension of the solution space of the homogeneous system

Ax = 0?
Mathematics
1 answer:
pshichka [43]2 years ago
5 0

Answer:

Dimension of the solution space of the homogeneous system =dimension of kernel=3.

Step-by-step explanation:

Given  a matrix has 3 rows and 5 columns .

Dimension of Domain=Number of columns in the matrix=5d

Dimension of the row space =2d

We know that dimension of row space= rank of matrix=2d

Rank-nullity theorem : Rank+nullity= dimension of domain=Number of columns in the matrix.

By using rank-nullity theorem

2+nullity=5

Nullity=5-2

Nullity=3

Dimension of kernel=3d

Dimension of kernel=Dimension of  solution space

Dimension of solution space=3d

Hence, the dimension of solution space of the homogeneous system =3d.

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265/5 = 53/1

53 miles per hour. 

*I hope this helped!
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rosijanka [135]

Answer:

\boxed{(-1, 0)}

Step-by-step explanation:

x² + 2x - 3 + y²  = 5

Strategy:

Convert the equation to the centre-radius form:

(x - h)² + (y - k)² = r²

The centre of the circle is at (h, k) and the radius is r .

Solution:

Move the number to the right-hand side.

x² + 2x + y²  = 8

Complete the square for x

(Take half the coefficient of x, square it, and add to each side of the equation)

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Complete the square for y

The coefficient of y is zero.

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Express the result as the sum of squares

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The centre of the circle is at \boxed{(-1,0)}

The graph of the circle below has its centre at (-1,0) and radius 3.

4 0
2 years ago
Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours. At this rate of growth, how many bacteria will
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The number of bacteria grown in 32 hours is 15771

<u>Step-by-step explanation:</u>

It is given that,

Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours.

Therefore, the bacteria has grown from 100 to 7000 in 14 hours.

<u> To calculate number of bacteria grown in 14 hours :</u>

⇒ 7000 - 100 = 6900

6900 bacteria grows in 14 hours. We need to find out the growth of bacteria in 1 hour in order to calculate its growth in 32 hours.

<u>To calculate number of bacteria grown in 1 hour :</u>

⇒ Total bacteria growth in 14 hours / 14

⇒ 6900 / 14

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<u>To calculate number of bacteria grown in 32 hours :</u>

⇒ 492.85 × 32

⇒ 15771.2

⇒ 15771  (rounded to nearest whole number)

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To determine the part of the triangle that corresponds to the parts of the other triangle, we can just see how they are arranged in the equation,
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kolezko [41]

Answer:

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