If A and B are matrices and AB = I, which of the following represents the value of B?
2 answers:
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] ](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%0A)
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]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-4%5C%5C3%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20)
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]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Cfrac%7B8%7D%7B4%7D%20%26%20%5Cfrac%7B-4%7D%7B4%7D%20%5C%5C%20%20%5Cfrac%7B3%7D%7B4%7D%20%26%20%5Cfrac%7B-1%7D%7B4%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
the simplified inverse matrix B is;
![\left[\begin{array}{ccc} 2 & -1 \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%202%20%26%20-1%20%5C%5C%20%5Cfrac%7B3%7D%7B4%7D%20%26%20%5Cfrac%7B-1%7D%7B4%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
the matrix A has been given
if we put symbols for the numbers in matrix A as shown below;
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
and then have to divide all the terms in matrix by determinant (4)
the simplified inverse matrix B is;
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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., = 35 and
= 6. We know that the probability density function for a normal distribution with a mean of
and a standard deviation of
is given by
in this case we have
Let 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 such that
=
, this number is
=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 such that
=
, this number is
=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
=
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
=
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)
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.