Problem 73
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 in the first matrix is not equal to the number of rows in the second matrix.
1Step 1: Understand the rule of matrix multiplication
Matrix multiplication is not simply element-by-element multiplication, it requires a specific condition to be met: The number of columns in the first matrix must be equal to the number of rows in the second matrix. Notably, the matrices multiplication is denoted as A * B, where A is an m×n matrix and B is a p×q matrix. For the multiplication to be defined, n (the number of columns in A) has to be equal to p (the number of rows in B).
2Step 2: When multiplication of two matrices is not defined
If the number of columns in the first matrix (A) is not equal to the number of rows in the second matrix (B), then the multiplication of matrices A and B is not defined. In other words, if A is an m×n matrix and B is a p×q matrix, and if n ≠ p, then A * B is not defined.
Other exercises in this chapter
Problem 72
Write each system in the form \(A X=B\). Then solve the system by entering \(A\) and \(B\) into your graphing utility and computing \(A^{-1} B\). $$\left\\{\beg
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Write each system in the form \(A X=B\). Then solve the system by entering \(A\) and \(B\) into your graphing utility and computing \(A^{-1} B\). $$\left\\{\beg
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