Final answer:
To find the values of m and n when A = 32, we can substitute the value of A into the equation A² = mA + nA and solve for m and n. The values of m and n are m = 32 - n and n = 32 - m.
Step-by-step explanation:
To find the values of m and n, we are given that A = 32 and A² = mA + nA. We can substitute the value of A into the equation and solve for m and n.
A² = mA + nA
(32)² = m(32) + n(32)
1024 = 32m + 32n
We can divide both sides of the equation by 32 to isolate m and n.
32m + 32n = 1024
m + n = 32
Therefore, the values of m and n that satisfy these equations are m = 32 - n and n = 32 - m.
For example, if we let m = 5, then n = 32 - 5 = 27.