) Let A = (1,2), B = (-3,4) , then A+B=(-2,6), A-B = (4,-2), -3A=(-3,-6)
2) Let X = (1, 0, π, 4), Y = (2, 4,-2π,-6), then 2X+Y = (4, 4, 0, 2) and
X-(1/2) Y = (0,-2, 2π, 7).
1) Correct calculations:
A+B = (1+(-3),2+4) = (-2,6)
A-B = (1-(-3),2-4) = (4,-2)
-3A = (-3*1,-3*2) = (-3,-6)
2) Correct calculations:
2X+Y = (2*1+2,2*0+4,2*π+(-2π),2*4+(-6)) = (4,4,0,2)
X-(1/2) Y = (1-1,0-2*(1/2),π-(-π/2),4-(-3)) = (0,-2,2π,7)
1) To find A + B, simply add the corresponding components of A and B:
A + B = (1 + (-3), 2 + 4)
= (-2, 6)
To find A - B, subtract the corresponding components of B from A:
A - B = (1 - (-3), 2 - 4)
= (4, -2)
To find -3A, multiply each component of A by -3:
-3A = (-3 * 1, -3 * 2)
= (-3, -6)
Therefore, A + B = (-2, 6), A - B = (4, -2), and -3A = (-3, -6).
2) To find 2X + Y, multiply each component of X by 2 and add the corresponding components of Y:
2X + Y = (2 * 1 + 2, 2 * 0 + 4, 2 * π + (-2π), 2 * 4 + (-6))
= (4, 4, 0, 2)
To find X - (1/2)Y, multiply each component of Y by (1/2) and subtract the resulting components from X:
X - (1/2)Y = (1 - (1/2) * 2, 0 - (1/2) * 4, π - (1/2) * (-2π), 4 - (1/2) * (-6))
= (0, -2, 2π, 7)
Therefore, 2X + Y = (4, 4, 0, 2) and X - (1/2)Y = (0, -2, 2π, 7).