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3 years ago

6 degrees above normal

Mathematics

1 answer:

TEA [102]3 years ago

7 0

Answer: Were the question at though

Step-by-step explanation:

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Find the? inverse, if it? exists, for the given matrix. [4 3] [3 6]

True [87]

Answer:

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Step-by-step explanation:

The inverse of a square matrix $A$ is $A^{-1}$ such that

$A A^{-1}=I$ where I is the identity matrix.

Consider, $A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right]$

$\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}$

$\det \begin{pmatrix}4&3 \\3&6\end{pmatrix}\ne 0$

$\mathrm{Find\:2x2\:matrix\:inverse\:according\:to\:the\:formula}:\quad \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$

$=\frac{1}{\det \begin{pmatrix}4&3\\ 3&6\end{pmatrix}}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc$

$4\cdot \:6-3\cdot \:3=15$

$=\frac{1}{15}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

4 0

3 years ago

Two counters are selected at random from a bag containing 5 red counters and 3 blue counters.

azamat

Answer:

1.4

Step-by-step explanation:

Probability of selecting a red counter :

Number of red counter / total number of counters

5 / (5 + 3) = 5 /8 = 0.625

Probability of selecting a blue counter = 0.375

Let number of red counters :

0, 1 or 2

0 red counters :

Expected value = x * p(x)

0 + (0.625*1) + (0.390625 * 2)

0 + 0.625 + 0.78125 = 1.40625

Expected number of red counters = 1.4

6 0

3 years ago

If the area of a rectangle is 144 sq. in. and the length of one side is 18in. what is the length of the other side?

navik [9.2K]

Hello from MrBillDoesMath!

Answer: The other side has a length of 8

Discussion:

Area of a rectangle = l * w ( length times width). In our case

Area = 144 = l * w = 18 * w =>

18 w = 144 =>

w = 144/18 = 8

Thank you,

MrB

8 0

3 years ago

Is there a relationship between the different of the integers and the distance between them?

user100 [1]

Wait just a minute. Hold up. Hee haw. Whoa !

Coming down to Earth for just a second ... what in the world is
the "distance" between integers anyway !

7 0

3 years ago

Read 2 more answers

Find the area of a regular hexagon

xxMikexx [17]

<h2>Answer:</h2><h2>42 cm^2</h2>

please see the attached picture for full solution

hope it helps...

Good luck on your assignment....

4 0

3 years ago

6 degrees above normal​

6 degrees above normal