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drek231 [11]
2 years ago
13

If A is a square matrix of order 2, then det(-3A) is *

Mathematics
2 answers:
Vsevolod [243]2 years ago
6 0

Answer:

c. 9 det A

Step-by-step explanation:

Given the following data;

Since A is a square matrix of order 2, we know that n = 2

K = 3

For any scalar k;

∣kA∣ = k^{n} ∣A∣

<em>Substituting into the equation;</em>

∣-3A∣ = -3²∣A∣

Simplifying, we have;

∣-3A∣ = 9∣A∣

= 9 detA

<em>Therefore, det (-3A) = 9 detA</em>

Angelina_Jolie [31]2 years ago
4 0

Answer:

free points :D

Step-by-step explanation:

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Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar
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The distance between the two points is d=8.6m

The polar coordinate of A is \left(4.47,296.57\right)

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The distance between two points is given by,

d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6

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The polar coordinates of A can be written as (Distance, tan^{-1} \frac{y}{x} )

Distance = \sqrt{x^{2} +y^{2} }

Substituting A(2,-4), we get,

Distance = \sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47

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To make the angle positive, let us add 360,

\theta=360-63.43=296.57

The polar coordinate of A is \left(4.47,296.57\right)

Similarly, The polar coordinate of B can be written as (Distance, tan^{-1} \frac{y}{x} )

Distance = \sqrt{x^{2} +y^{2} }

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tan^{-1} \frac{y}{x} =tan^{-1} \frac{3}{-3}=-45

To make the angle positive, let us add 360,

\theta=180-45=135^{\circ}

The polar coordinate of B is \left(4.24,135\right)

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3 years ago
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3 years ago
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