2/for the linear system defined by Ax=B where A and B are given below (a=20 and b = 47) 2a 3 a 7 b 6. 9 4 8 -2 A = 6 [(45 + 10a)] (54 + 7b) 2 В — 19 38 Solve the linear system to determine the vector x using the Gauss Elimination method, presenting the full computational transformation steps

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2/for the linear system defined by Ax=B where A and B are given below (a=20 and b = 47)
2а 3
a
7
b
9 4
0 6
[(45 + 10a)]
(54 + 7b)
6.
8
A =
-2
B =
В
19
38
Solve the linear system to determine the vector x using the Gauss Elimination method, presenting the
full computational transformation steps
3/
Calculate the dot product h, (h = cx d) and the k-directed product vector of c and d, (k = cx d ) where c,
d are the two vectors given by (a=20 and b=47)
c = [aỉ + bj+ 2a k ],d
= [ai +2j+ bk]
Transcribed Image Text:2/for the linear system defined by Ax=B where A and B are given below (a=20 and b = 47) 2а 3 a 7 b 9 4 0 6 [(45 + 10a)] (54 + 7b) 6. 8 A = -2 B = В 19 38 Solve the linear system to determine the vector x using the Gauss Elimination method, presenting the full computational transformation steps 3/ Calculate the dot product h, (h = cx d) and the k-directed product vector of c and d, (k = cx d ) where c, d are the two vectors given by (a=20 and b=47) c = [aỉ + bj+ 2a k ],d = [ai +2j+ bk]
4/
We have (a=20 and b=47) and the function f(x, y, z) = 6x² + 4y²x – 7zy2
a. Calculate the gradient of the function f at P(2a,-b,5)
b. Determine the direction of variation of the function f at P(a,b,3a) in the direction of vector c = [2,5,a]
c. The application, assuming the need to optimize the function f to the minimum value, calculates the
values of the variables after updating 1 time with an update rate of 0.1
5/
A line in the factory is driven by 2 motors. Conveyor belt allows 100kg load. If the load exceeds 100kg,
the probability of motor 1 failure is a%, the possibility of motor 2 failure is up to 2*b%. The probability
of both motors failing is 0.5a%. When the system is in operation and the employee loads the conveyor
with a load of 120kg. Calculate the probability that motor 1 or motor 2 fails in this case.
(a=20 and b =47)
Transcribed Image Text:4/ We have (a=20 and b=47) and the function f(x, y, z) = 6x² + 4y²x – 7zy2 a. Calculate the gradient of the function f at P(2a,-b,5) b. Determine the direction of variation of the function f at P(a,b,3a) in the direction of vector c = [2,5,a] c. The application, assuming the need to optimize the function f to the minimum value, calculates the values of the variables after updating 1 time with an update rate of 0.1 5/ A line in the factory is driven by 2 motors. Conveyor belt allows 100kg load. If the load exceeds 100kg, the probability of motor 1 failure is a%, the possibility of motor 2 failure is up to 2*b%. The probability of both motors failing is 0.5a%. When the system is in operation and the employee loads the conveyor with a load of 120kg. Calculate the probability that motor 1 or motor 2 fails in this case. (a=20 and b =47)
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