What are the dimensions of the matrix product?

Question

UpStudy AI · Accepted Answer

To determine the dimensions of a matrix product, we need to consider the dimensions of the matrices involved in the multiplication.

1. **Matrix Dimensions**: 
   - If matrix $$ A $$ has dimensions $$ m 	imes n $$ (m rows and n columns) and matrix $$ B $$ has dimensions $$ n 	imes p $$ (n rows and p columns), then the product $$ AB $$ is defined.

2. **Resulting Dimensions**:
   - The resulting matrix $$ AB $$ will have dimensions $$ m 	imes p $$. This means the number of rows in the resulting matrix is equal to the number of rows in the first matrix $$ A $$, and the number of columns in the resulting matrix is equal to the number of columns in the second matrix $$ B $$.

3. **Condition for Multiplication**:
   - The multiplication is only defined if the number of columns in the first matrix $$ A $$ (which is $$ n $$) is equal to the number of rows in the second matrix $$ B $$ (also $$ n $$).

In summary, if $$ A $$ is $$ m 	imes n $$ and $$ B $$ is $$ n 	imes p $$, then the product $$ AB $$ will have dimensions $$ m 	imes p $$.
The matrix product $$ AB $$ has dimensions $$ m 	imes p $$, where $$ A $$ is $$ m 	imes n $$ and $$ B $$ is $$ n 	imes p $$.

What are the dimensions of the matrix product?

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions