Problem 60
Question
Describe when the multiplication of two matrices is not defined.
Step-by-Step Solution
Verified Answer
The multiplication of two matrices is not defined when the number of columns of the first matrix doesn't equal the number of rows of the second matrix.
1Step 1: Defining matrix multiplication
Matrix multiplication of two matrices A and B is defined only when the number of columns of A (let's denote it as 'n') is equal to the number of rows of B (denoted as 'm'). In other words, if A is of size p×n and B is of size n×m, then the multiplication is defined, and the result will be a new matrix of size p×m.
2Step 2: When multiplication is not defined
If the number of columns of the first matrix is not equal to the number of rows of the second matrix, then the multiplication is not defined. For example, if matrix A is of size p×n and matrix B is of size m×q, and if n ≠ m, the product AB does not exist.
Other exercises in this chapter
Problem 59
Describe how to multiply matrices.
View solution Problem 59
Use a graphing utility to find the multiplicative inverse of each matrix. Check that the displayed inverse is correct. $$ \left[\begin{array}{rrr} -2 & 1 & -1 \
View solution Problem 60
Use a graphing utility to evaluate the determinant for the given matrix. $$ \left[\begin{array}{rrrr}3 & -2 & -1 & 4 \\\\-5 & 1 & 2 & 7 \\\2 & 4 & 5 & 0 \\\\-1
View solution Problem 60
Use a graphing utility to find the multiplicative inverse of each matrix. Check that the displayed inverse is correct. $$ \left[\begin{array}{rrr} 1 & 1 & -1 \\
View solution