If A and B are vectors such that
A+3B=-3+j & A-B=i-2j
then find A&B?
A+3B = -3i+j
A-B = i - 2j
subtract and you get
4B = -4i+3j
B = -i + 3/4 j
A = B+i-2j = (-i+3/4 j)+(i-2j) = 0i - 5/4 j
are you sure
well, I did check to see that they satisfied the original equations.
Didn't you?
To find the vectors A and B, we can solve the given system of equations. Let's start by rearranging the equations and isolating A and B.
Given:
A + 3B = -3 + j ---(1)
A - B = i - 2j ---(2)
To eliminate A, we can multiply equation (2) by 3 and add it to equation (1):
3(A - B) = 3(i - 2j)
3A - 3B = 3i - 6j ---(3)
Now we can add equation (3) to equation (1):
(A + 3B) + (3A - 3B) = (-3 + j) + (3i - 6j)
4A = 3i - 5j - 3
To isolate A, we divide both sides of the equation by 4:
A = (3i - 5j - 3) / 4
Now that we have the value of A, we can substitute it back into equation (1) to find B:
(3i - 5j - 3) / 4 + 3B = -3 + j
Rearranging the equation to isolate B:
3B = -3 + j - (3i - 5j - 3) / 4
Simplifying the equation:
3B = -3 + j - (3i - 5j - 3) / 4
Finally, to find the value of B, we divide the entire equation by 3:
B = (-3 + j - (3i - 5j - 3) / 4) / 3
Therefore, we have found the values of A and B in terms of i and j.