# Finding the matrix

• Nov 15th 2009, 02:18 PM
racewithferrari
Finding the matrix
Suppose A is a 4X2 matrix, B is a 5X4 matrix, and C is a 2X5 matrix.
For each of the following product expressions, indicate whether the
matrix product is defined, and, if so, the dimensions of the product.
(1.5 pts.)

Defined? Dimensions
------------------------------------------
AB | |
AC | |
BA | |
BC | |
CA | |
CB | |
• Nov 15th 2009, 02:29 PM
emakarov
The product is defined when the width of the left factor is equal to the height of the right one. The resulting product has the height of the left factor and the width of the right one.
• Nov 15th 2009, 02:40 PM
Plato
Quote:

Originally Posted by racewithferrari
Suppose A is a 4X2 matrix, B is a 5X4 matrix, and C is a 2X5 matrix.
For each of the following product expressions, indicate whether the
matrix product is defined, and, if so, the dimensions of the product.
(1.5 pts.) |

For matrices $\displaystyle A~\&~B$ the product $\displaystyle A_{k,j} B_{m,n}$ exists if and only if $\displaystyle j=m$.
The dimension of $\displaystyle A\cdot B$ is $\displaystyle k\times n$.
• Nov 16th 2009, 02:45 PM
racewithferrari
Can you elaborate your answer in an easy way so that I can understand, because I am new to this and I don't want my teacher to think that I have cheated.
• Nov 16th 2009, 03:29 PM
Plato
Quote:

Originally Posted by racewithferrari
Can you elaborate your answer in an easy way so that I can understand, because I am new to this and I don't want my teacher to think that I have cheated.

Examples
If $\displaystyle A_{3,4}~\&~B_{4,2}$ then $\displaystyle A\cdot B=C_{3,2}$

BUT $\displaystyle B\cdot A$ does not exist because $\displaystyle 2\ne 3$.