Determine whether the statement below is true or false. Justify the answer. Each elementary matrix is invertible. Choose the correct answer below. O A. The statement is true. Since every invertible matrix is a product of elementary matrices, every elementary matrix must be invertible. B. The statement is false. It is possible to perform row operations on an nxn matrix that do not result in the identity matrix. Therefore, not every elementary matrix is invertible. O C. The statement is true. Since each elementary matrix corresponds to a row operation, and every row operation is reversible, every elementary matrix has an inverse matrix. O D. The statement is false. Every matrix that is not invertible can be written as a product of elementary matrices. At least one of those elementary matrices is not invertible.
Determine whether the statement below is true or false. Justify the answer. Each elementary matrix is invertible. Choose the correct answer below. O A. The statement is true. Since every invertible matrix is a product of elementary matrices, every elementary matrix must be invertible. B. The statement is false. It is possible to perform row operations on an nxn matrix that do not result in the identity matrix. Therefore, not every elementary matrix is invertible. O C. The statement is true. Since each elementary matrix corresponds to a row operation, and every row operation is reversible, every elementary matrix has an inverse matrix. O D. The statement is false. Every matrix that is not invertible can be written as a product of elementary matrices. At least one of those elementary matrices is not invertible.
Determine whether the statement below is true or false. Justify the answer. Each elementary matrix is invertible. Choose the correct answer below. O A. The statement is true. Since every invertible matrix is a product of elementary matrices, every elementary matrix must be invertible. B. The statement is false. It is possible to perform row operations on an nxn matrix that do not result in the identity matrix. Therefore, not every elementary matrix is invertible. O C. The statement is true. Since each elementary matrix corresponds to a row operation, and every row operation is reversible, every elementary matrix has an inverse matrix. O D. The statement is false. Every matrix that is not invertible can be written as a product of elementary matrices. At least one of those elementary matrices is not invertible.
Transcribed Image Text:**Determine whether the statement below is true or false. Justify the answer.**
Each elementary matrix is invertible.
**Choose the correct answer below.**
- A. The statement is true. Since every invertible matrix is a product of elementary matrices, every elementary matrix must be invertible.
- B. The statement is false. It is possible to perform row operations on an n × n matrix that do not result in the identity matrix. Therefore, not every elementary matrix is invertible.
- C. The statement is true. Since each elementary matrix corresponds to a row operation, and every row operation is reversible, every elementary matrix has an inverse matrix.
- D. The statement is false. Every matrix that is not invertible can be written as a product of elementary matrices. At least one of those elementary matrices is not invertible.
The correct choice is indicated next to option A with a filled circle.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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