SOLUTION: Let X, Y and Z be matrices of sizes 2x3, 4x3 and 1x4, respectively. Then the size of (XY)^T(Z)^T (where ^T denotes transpose of a matrix) is (2x1) The answer to the question is

Algebra ->  Matrices-and-determiminant -> SOLUTION: Let X, Y and Z be matrices of sizes 2x3, 4x3 and 1x4, respectively. Then the size of (XY)^T(Z)^T (where ^T denotes transpose of a matrix) is (2x1) The answer to the question is       Log On


   

Question 307330: Let X, Y and Z be matrices of sizes 2x3, 4x3 and 1x4, respectively. Then the size of (XY)^T(Z)^T (where ^T denotes transpose of a matrix) is (2x1)
The answer to the question is 2x1, but I don't understand how to get that answer.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you meant to write XY%5ET%2AZ%5ET


First off, Y%5ET is a 3x4 matrix (since the transpose flips the rows and columns). So XY%5ET is a 2x4 matrix since the product of an m x n and an n x r matrix is an m x r matrix. Also, Z%5ET is a 4x1 matrix (transposes swap rows and columns). So because XY%5ET is a 2x4 matrix and Z%5ET is a 4x1 matrix, this means that XY%5ET%2AZ%5ET is a 2x1 matrix.