Answer:
(A+B)(A+B)=A.A+B.A+A.B+B.B
Step-by-step explanation:
Given that matrices A and B are nxn matrices
We need to find (A+B)(A+B)
For understanding the multiplication of matrices let'take A is mxn and B is pxq matrices,we can multiple only when n=p,so our Ab matrices will be mxq.
We know that that in matrices AB is not equal to BA.
Now find
(A+B)(A+B)=A.A+B.A+A.B+B.B
So from we can say that (A+B)(A+B) is not equal to A.A+2B.A+B.B because AB is not equal to BA in matrices.
So (A+B)(A+B)=A.A+B.A+A.B+B.B
Using the triangle of pascal we have that the expression equivalent to (x + y) ^ 6 is given by:
x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
Therefore, the coefficients of the expansion are given by:
1, 6, 15, 20, 15, 6, 1
Answer:
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1
Answer:
37 and -18
Step-by-step explanation:
Let one number be x and other y
1 x + 1 y = 19 .............1
1 x -1 y = 55 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by 1
1 x 1 y = 19
1 x + -1 y = 55
Add the two equations
2 x = 74
/ 2
x = 37
plug value of x in (1)
1 x + 1 y = 19
37 + 1 y = 19
1 y = 19 -37
1 y = -18
y = -18
37 and -18
Let x represent the speed of of boat.
We have been given that the river current is 3 miles per hour.
The speed of boat upstream will be .
The speed of boat downstream would be .
We have been given that you travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a dock.
We can represent this information in an equation as:
Since the speed of the boat is 18 miles per hour, so we will substitute in above equation and solve for time.
Since time is in hours, so let us convert our given time in minutes.
1 hour = 60 minutes.
Rounding to nearest tenth of minute.
Therefore, it will take approximately 17.7 minutes for the boat to take the trip.