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jok3333 [9.3K]
3 years ago
5

If A and B are matrices and AB = I, which of the following represents the value of B?

Mathematics
2 answers:
Ratling [72]3 years ago
6 0
If the product of 2 matrices are I this means that B is inverse matrix of A.
the matrix A has been given 
if we put symbols for the numbers in matrix A as shown below;
\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] 

we need to first find the determinant (D)
D = ad - bc
where a = -1 , b = 4, c = -3 and d = 8
substituting these values 
D = -1x8 - (4x-3)
   = -8 +  12 = 4 
to find the inverse we need to exchange a and d and then multiply both b and c by -1
\left[\begin{array}{ccc}8&-4\\3&-1\\\end{array}\right]
and then have to divide all the terms in matrix by determinant (4)
\left[\begin{array}{ccc} \frac{8}{4} & \frac{-4}{4} \\  \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]
the simplified inverse matrix B is;
\left[\begin{array}{ccc} 2 & -1 \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]

Stels [109]3 years ago
5 0

Answer:

4th option D

Step-by-step explanation:

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Step-by-step explanation:

In a right angle triangle one angle is 90°

w.k.t sum of angles in a triangle is 180°

thus, 2x+15+x+90°=180°

3x+105°=180°

3x=75°

x= 75/3=25°

Hope this helps you.

7 0
3 years ago
The scatter plot shows the number of people at a fair based on the outside temperature. How many fewer people would be predicted
frez [133]

Answer

1.-0.08

Step-by-step explanation:

6 0
3 years ago
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2. The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of
IgorC [24]

Answer:

a) 37.31 b) 42.70 c) 0.57 d) 0.09

Step-by-step explaanation:

We are regarding a normal distribution with a mean of 35 and a standard deviation of 6, i.e., \mu = 35 and \sigma = 6. We know that the probability density function for a normal distribution with a mean of \mu and a standard deviation of \sigma is given by

f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]

in this case we have

f(x) = \frac{1}{\sqrt{2\pi}6}\exp[-\frac{(x-35)^{2}}{2(6^{2})}]

Let X be the random variable that represents a row score, we find the values we are seeking in the following way

a)  we are looking for a number x_{0} such that

P(X\leq x_{0}) = \int\limits^{x_{0}}_{-\infty} {f(x)} \, dx = 0.65, this number is x_{0}=37.31

you can find this answer using the R statistical programming languange and the instruction qnorm(0.65, mean = 35, sd = 6)

b) we are looking for a number  x_{1} such that

P(X\leq x_{1}) = \int\limits^{x_{1}}_{-\infty} {f(x)} \, dx = 0.9, this number is x_{1}=42.70

you can find this answer using the R statistical programming languange and the instruction qnorm(0.9, mean = 35, sd = 6)

c) we find this probability as

P(28\leq X\leq 38)=\int\limits^{38}_{28} {f(x)} \, dx = 0.57

you can find this answer using the R statistical programming languange and the instruction pnorm(38, mean = 35, sd = 6) -pnorm(28, mean = 35, sd = 6)

d) we find this probability as

P(41\leq X\leq 44)=\int\limits^{44}_{41} {f(x)} \, dx = 0.09

you can find this answer using the R statistical programming languange and the instruction pnorm(44, mean = 35, sd = 6) -pnorm(41, mean = 35, sd = 6)

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3 years ago
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How many medians a triangle can have?
OverLord2011 [107]

\qquad \qquad\huge \underline{\boxed{\sf Answer}}

Medians are the line segments that divides a side of Triangle into two equal parts, each having equal length. and since triangles have 3 sides, they have 3 medians as well.

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4/10. *. 3/9. = 12/90 = 2/15
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