Matrix Multiplication Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Can you multiply a 2ร—32 \times 3 matrix by a 2ร—32 \times 3 matrix? Why or why not?

Solution

  1. 1
    Inner dimensions: columns of first (3) โ‰  rows of second (2).
  2. 2
    Not compatible. Matrix multiplication requires columns of AA = rows of BB.

Answer

No, the dimensions are incompatible.
For ABAB to be defined, the number of columns in AA must equal the number of rows in BB. Here 3โ‰ 23 \neq 2, so the product is undefined.

About Matrix Multiplication

Multiplying matrices AA (mร—nm \times n) and BB (nร—pn \times p) by taking dot products of rows of AA with columns of BB to produce an mร—pm \times p result.

Learn more about Matrix Multiplication โ†’

More Matrix Multiplication Examples

Example 1 medium

Compute [formula].

Example 2 hard

Compute [formula].

Example 4 medium

Compute [formula].

โ† All Matrix Multiplication Examples Matrix Multiplication Concept