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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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