Answer:
Step-by-step explanation:
We are given the matrix
![A = \left[\begin{matrix}4&0&0 \\ 1&3&0 \\-2&3&-1 \end{matrix}\right]](https://tex.z-dn.net/?f=%20A%20%3D%20%5Cleft%5B%5Cbegin%7Bmatrix%7D4%260%260%20%5C%5C%201%263%260%20%5C%5C-2%263%26-1%20%5Cend%7Bmatrix%7D%5Cright%5D%20)
a) To find the characteristic polynomial we calculate 
where I is the identity matrix of appropiate size. in this case the characteristic polynomial is
Since this matrix is upper triangular, its determinant is the multiplication of the diagonal entries, that is
which is the characteristic polynomial of A.
b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are 
c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression 
and solve the system 
by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.
Consider 
. We get the matrix
![\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Bmatrix%7D0%260%260%20%5C%5C%201%26-1%260%20%5C%5C-2%263%26-5%20%5Cend%7Bmatrix%7D%5Cright%5D%20)
The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by
So, the base for this eigenspace is the vector (5,5,1).
If 
then the base is (0,4,3) and if 
then the base is (0,0,1)
$81.00
30% of 270 = 0.3 × 270 = 81
Answer:
8.2+/-0.25
= ( 7.95, 8.45) years
the 95% confidence interval (a,b) = (7.95, 8.45) years
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 8.2 years
Standard deviation r = 1.1 years
Number of samples n = 75
Confidence interval = 95%
z value(at 95% confidence) = 1.96
Substituting the values we have;
8.2+/-1.96(1.1/√75)
8.2+/-1.96(0.127017059221)
8.2+/-0.248953436074
8.2+/-0.25
= ( 7.95, 8.45)
Therefore the 95% confidence interval (a,b) = (7.95, 8.45) years
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Answer:
Hope it helps u
Step-by-step explanation:
As we know that ,
Mean = sum of the terms/ numbers of terms
But here grouped data is given so , we use the formula
Mean=∑[f. m]/ ∑f
where f is frequency and m is mid point of each height ,
Now first we have to find the mid point of each interval, where
midpoint of each interval = (lower boundary + upper boundary)/2
m1=(150+154)/2 = 152
m2=(155+159)/2= 157,now found other by same formula, for each interval
m3= 162
m4= 167
m5=172 Now we find the midpoint of each interval ,so now
∑[f. m]=f1*m1+f2*m2+f3*m3+f4*m4+f5*m5
now putting the values of each frequency for given interval and midpoint of each interval we will get,
∑[f. m]=456+942+1296+167*x+344 = 167*x+3038
Now find,
∑f=f1+f2+f3+f4+f5
∑f=19+x
Now we have,
∑[f. m]=167*x+3038
∑f=19+x
also given mean height=161.6 cm
putt these values in above equation we get,
161.6=
now solve this ,
161.6(19+x)=167*x+3038
3070.4+161.6*x=167*x+3038
3070.4-3038=167*x-161.6*x
32.4=5.4*x
x=32.4/5.4
<h2>
x=6 Ans........</h2>
