SOLUTION: Suppose A is a 5 x 3 matrix, B is an r x s matrix and C is a 4 x 5 matrix. If At BC is defined, which one is true? ( the t after A means inverse) 1) the size of At BC is 3 x 5

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Suppose A is a 5 x 3 matrix, B is an r x s matrix and C is a 4 x 5 matrix. If At BC is defined, which one is true? ( the t after A means inverse) 1) the size of At BC is 3 x 5       Log On


   

Question 575851: Suppose A is a 5 x 3 matrix, B is an r x s matrix and C is a 4 x 5 matrix. If At BC is defined, which one is true? ( the t after A means inverse)
1) the size of At BC is 3 x 5
2) r = 2, s = 5
3) r = 3, s = 4
4) r = 3, s = 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order for BC to be defined, B must have 4 columns. So s = 4. This means that the resulting matrix BC is a r x 5 matrix


Matrix A is a 5 x 3 matrix. So A%5ET is a 3 x 5 matrix since the transpose flips the rows and columns.


So BC must have 5 rows in order for A%5ET%2ABC to be defined. This therefore means that A%5ET%2ABC is a 3 x 5 matrix

So the answer is choice 1)