Are there two 3 by 3 matrices A and B, both of rank 2,such that AB is the zero matrix? Explain your answer.1
Question
Solution 1
Yes, there are two 3 by 3 matrices A and B, both of rank 2, such that AB is the zero matrix. Here is the explanation:
Step 1: Understand the concept of rank The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. A 3 by 3 matrix of rank 2 means that there a Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI
Similar Questions
Are there two 3 by 3 matrices A and B, both of rank 2,such that AB is the zero matrix? Explain your answer
If A and B are 3 × 3 real matrices such that rank(AB) = 1, then rank(BA) cannot be
Suppose A is an m × n matrix and B is an n × p matrix. Show thatCol AB ⊆ Col A and Nul B ⊆ Nul AB.Hence, rank (AB) ≤ rank A and rank (AB) ≤ rank B.
Suppose P and Q are two different matrices of order 3 × n and n × p , thenthe order of the matrix P × Q is?
Are the two matrices similar? If so, find a matrix P such that B = P−1AP. (If not possible, enter IMPOSSIBLE.)A = 2 0 0 0 1 00 0 3 B = 1 0 0 0 2 00 0 3
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.