Question

If A = [8 -3] and B = [4 -5]; find A + B and B – A.​

a) A+B=[12 −8], B−A=[−4 2]
b) A+B=[4 −8], B−A=[−4 2]
c) A+B=[12 −2], B−A=[−4 −2]
d) A+B=[12 −8], B−A=[4 2]

Answer 1

After adding and subtracting the corresponding elements of vectors A and B, the results are A + B = [12, -8] and B - A = [-4, -2].

Step-by-step explanation:

To find A + B and B − A, we will perform vector addition and subtraction. Vector addition is straightforward while for subtraction, we will add A to the negative of B, as vector subtraction is the addition of a negative vector.

Given A = [8, -3] and B = [4, -5].

For A + B:

Sum the corresponding elements:

[8 + 4, -3 + (-5)]

This gives us: [12, -8]

For B − A:

Subtract the corresponding elements of A from B: [4 - 8, -5 - (-3)]

This simplifies to: [-4, -5 + 3]Which gives us: [-4, -2]

Therefore, the correct answers are A + B = [12, -8] and B − A = [-4, -2].