SOLUTION: Let A=[1. 2 3. a] and B=[1. 1 b 3] Under what condition AB=BA? a=b=1 a=1.5 and b=5 a=5. and b=1.5 None

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Let A=[1. 2 3. a] and B=[1. 1 b 3] Under what condition AB=BA? a=b=1 a=1.5 and b=5 a=5. and b=1.5 None      Log On


   

Question 1133535: Let A=[1. 2
3. a] and B=[1. 1
b 3]
Under what condition AB=BA?
a=b=1
a=1.5 and b=5
a=5. and b=1.5
None
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


A = matrix%282%2C2%2C1%2C2%2C3%2Ca%29
B = matrix%282%2C2%2C1%2C1%2Cb%2C3%29

AB = matrix%282%2C2%2C1%2C2%2C3%2Ca%29 * matrix%282%2C2%2C1%2C1%2Cb%2C3%29 = matrix%282%2C2%2C2b%2B1%2C7%2C3%2Bab%2C3%2B3a%29

BA = matrix%282%2C2%2C1%2C1%2Cb%2C3%29 * matrix%282%2C2%2C1%2C2%2C3%2Ca%29 = matrix%282%2C2%2C4%2Ca%2B2%2Cb%2B9%2C2b%2B3a%29

The two product matrices are equivalent if all the corresponding elements are the same:

2b+1 = 4
7 = a+2
3+ab = b+9
3+3a = 2b+3a

There is a pair of values for a and b for which that system of equations is consistent; and it is one of the answer choices.

I leave it to you to do the rest of the work to find which one....