Question

1. Show that the following statement is false: if the matrix equation Ax=b has solutions, then the equation (A^T)x=c must also have solutions. A can be any matrix, A^T is its transpose, b and c are any vectors of compatible size. You should produce a matrix A such that Ax=b has solutions, but (A^T)x=c does not. 2. Post your matrix A to the discussion board, along with a brief explanation of why your matrix works.

Name: 1. Show that the following statement is false: if the matrix equation Ax=b has solutions, then the equation (A^T)x=c must also have solutions. A can be any matrix, A^T is its transpose, b and c are any vectors of compatible size. You should produce a matrix A such that Ax=b has solutions, but (A^T)x=c does not. 2. Post your matrix A to the discussion board, along with a brief explanation of why your matrix works.
Uploaded: 2022-07-25T06:18:49-08:00
Duration: 6 min 19 s
Channel: Adi S

          1. Show that the following statement is false: if the matrix equation Ax=b has solutions, then the equation (A^T)x=c must also have solutions. A can be any matrix, A^T is its transpose, b and c are any vectors of compatible size. You should produce a matrix A such that Ax=b has solutions, but (A^T)x=c does not. 2. Post your matrix A to the discussion board, along with a brief explanation of why your matrix works.

1. Show that the following statement is false: if the matrix equation Ax=b has solutions, then the equation (A^T)x=c must also have solutions. A can be any matrix, A^T is its transpose, b and c are any vectors of compatible size. You should produce a matrix A such that Ax=b has solutions, but (A^T)x=c does not. 2. Post your matrix A to the discussion board, along with a brief explanation of why your matrix works.

Added by Lorena K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/25/2022

Step 1

Let's choose the matrix A as follows: \[ A = \begin{pmatrix} 6 & 3 \\ 4 & 2 \end{pmatrix} \] This matrix is non-invertible because the determinant of A is 0. Show more…

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Show that the following statement is false: if the matrix equation Ax=b has solutions, then the equation (A^T)x=c must also have solutions. A can be any matrix, A^T is its transpose, b and c are any vectors of compatible size. You should produce a matrix A such that Ax=b has solutions, but (A^T)x=c does not.