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The matrix A is 4 x 4 and row reduces to the identity. The matrix B is 3 x 3 and the solution to B = b is a plane in R³. Include the following in your initial post: For A and B, answer the following questions: 1. Is the matrix invertible? How do you know? Use a theorem from the readings or videos. 2. What is the rank of the matrix? Justify your reasoning. 3. How many solutions are there to Ax=0? Explain how you know. Use a theorem from the reading or videos.

The matrix A is 4 x 4 and row reduces to the identity. The matrix B is 3 x 3 and the solution to B = b is a plane in R³. Include the following in your initial post: For A and B, answer the following questions: 1. Is the matrix invertible? How do you know? Use a theorem from the readings or videos. 2. What is the rank of the matrix? Justify your reasoning. 3. How many solutions are there to Ax=0? Explain how you know. Use a theorem from the reading or videos.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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Consider two matrices, A and B: The matrix A is 4 x 4 and row reduces to the identity. The matrix B is 3 x 3 and the solution to B = b is a plane in R³. Include the following in your initial post: For A and B, answer the following questions: 1. Is the matrix invertible? How do you know? Use a theorem from the readings or videos. 2. What is the rank of the matrix? Justify your reasoning. 3. How many solutions are there to Ax=0? Explain how you know. Use a theorem from the reading or videos.
Transcribed Image Text:Consider two matrices, A and B: The matrix A is 4 x 4 and row reduces to the identity. The matrix B is 3 x 3 and the solution to B = b is a plane in R³. Include the following in your initial post: For A and B, answer the following questions: 1. Is the matrix invertible? How do you know? Use a theorem from the readings or videos. 2. What is the rank of the matrix? Justify your reasoning. 3. How many solutions are there to Ax=0? Explain how you know. Use a theorem from the reading or videos.
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Can you please give a explanation of why the rank of B is 2 and how you find the rank and what is the definition. 

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