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amid [387]
3 years ago
12

If the null space of A4×5 is exactly a two-dimensional plane, answer the following:

Mathematics
1 answer:
Hatshy [7]3 years ago
8 0

Answer:

I.

A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4

Null space is exactly two dimensional plane

dim null (A) = 2

II.

Rank A = dim U - dim Null A = 5 - 2 = 3

III.

Number of linearly Independent columns of A is the rank of A = 3

IV.

Yes, The system Ax = b has no solution sometimes as range of A \neq V

V.

Yes,Sometimes Ax = b has a unique solution

VI.

Yes, sometimes Ax = b has infinitely many solutions

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PLEASE HELP ASAP
Ksenya-84 [330]
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 A=LxW
 
 A is the area of the photograph (A=54 in²).
 L is the lenght of the photograph (L=12-4x).
 W is the widht of the photograph (W=12-2x)
 
 2. When you substitute these values into the formula A=LxW, you obtain:
 
 A=LxW
 54=(12-4x)(12-2x)
 
 3. When you apply the distributive property, you have:
 
 54=144-24x-48x+8x²
 8x²-72x+144-54=0
 
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6 0
3 years ago
Find the reference angle for the given angle. Show your work. -404°
Mamont248 [21]

Answer:

44°

Step-by-step explanation:

The reference angle is the magnitude of the smallest angle between the terminal ray and the x-axis.

Your angle is one full circle clockwise plus 44° more (-360° -44° = -404°), so makes an angle of -44° with respect to the positive x-axis. The magnitude of that is 44°.

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<em>Using a function</em>

The attachment shows a calculator function that can be used to find the reference angle for any angle. (Replace the value -404 with the angle of your choice.)

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Answer:

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Step-by-step explanation:

The marks on the diagram show AE ≅ DE. We know vertical angles AEB and DEC are congruent, and we know alternate interior angles BAE and CDE are congruent. The congruent angles we have identified are on either end of the congruent segment, so the ASA theorem applies.

Matching corresponding vertices, we can declare ΔABE ≅ ΔDCE.

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The answer would be B
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eduard

Answer:

36

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473/13

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3 years ago
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