If a&b are vectors such that a+3b=-3i+j & a-b=i-2j then find vectors a&b.

subtract the equations:

4b=-4i+3j
solve for b. Then, solve the for a, using this solution for b.
Just algebra involved.

To find the vectors a and b, we will use a system of equations. Here's how we can solve it step by step:

Step 1: Write the given equations in the standard form.

a + 3b = -3i + j ---(Equation 1)
a - b = i - 2j ---(Equation 2)

Step 2: Solve Equation 2 for a in terms of b.

a = b + i - 2j ---(Equation 3)

Step 3: Substitute Equation 3 into Equation 1.

(b + i - 2j) + 3b = -3i + j

Step 4: Simplify the equation.

4b - 2i - 5j = -3i + j

Step 5: Group like terms.

4b - 2i + 5j = j - 3i

Step 6: Equate the coefficients of the i and j terms on both sides.

4b - 2i = -3i ----(Equation A)
5j = j ----(Equation B)

Step 7: Solve Equation B for j.

5j = j
4j = 0
j = 0

Step 8: Substitute the value of j back into Equation B.

5(0) = 0
0 = 0 (True)

Step 9: Since j = 0, we can substitute it into Equation A.

4b - 2i = -3i

Step 10: Move the variables to one side.

4b = -3i + 2i

Step 11: Simplify.

4b = -i

Step 12: Multiply both sides by (1/4) to solve for b.

b = (-1/4)i

Step 13: Substitute the value of b into Equation 3.

a = (-1/4)i + i - 2(0)
a = (3/4)i

So, the vectors a and b are:

a = (3/4)i
b = (-1/4)i