Determine whether the statement below is true or false. Justify the answer. If A is an invertible nxn matrix, then the equation Ax b is consistent for each b in R". Choose the correct answer below. O A. The statement is false. The matrix A is invertible if and only if A is row equivalent to the identity matrix, and not every matrix A satisfying Ax = b is row equiva to the identity matrix. O B. The statement is true. Since A is invertible, A b=x for all x in R". Multiply both sides by A and the result is Ax = b. O c. The statement is false. The matrix A satisfies Ax = b if and only if A is row equivalent to the identity matrix, and not every matrix that is row equivalent to the identity matrix is invertible. O D. The statement is true. Since A is invertible, A b exists for all b in R". Define x = A'b. Then Ax = b.
Determine whether the statement below is true or false. Justify the answer. If A is an invertible nxn matrix, then the equation Ax b is consistent for each b in R". Choose the correct answer below. O A. The statement is false. The matrix A is invertible if and only if A is row equivalent to the identity matrix, and not every matrix A satisfying Ax = b is row equiva to the identity matrix. O B. The statement is true. Since A is invertible, A b=x for all x in R". Multiply both sides by A and the result is Ax = b. O c. The statement is false. The matrix A satisfies Ax = b if and only if A is row equivalent to the identity matrix, and not every matrix that is row equivalent to the identity matrix is invertible. O D. The statement is true. Since A is invertible, A b exists for all b in R". Define x = A'b. Then Ax = b.
Determine whether the statement below is true or false. Justify the answer. If A is an invertible nxn matrix, then the equation Ax b is consistent for each b in R". Choose the correct answer below. O A. The statement is false. The matrix A is invertible if and only if A is row equivalent to the identity matrix, and not every matrix A satisfying Ax = b is row equiva to the identity matrix. O B. The statement is true. Since A is invertible, A b=x for all x in R". Multiply both sides by A and the result is Ax = b. O c. The statement is false. The matrix A satisfies Ax = b if and only if A is row equivalent to the identity matrix, and not every matrix that is row equivalent to the identity matrix is invertible. O D. The statement is true. Since A is invertible, A b exists for all b in R". Define x = A'b. Then Ax = b.
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer.
If A is an invertible nxn matrix, then the equation Ax = b is consistent for each b in R".
Choose the correct answer below.
O A. The statement is false. The matrix A is invertible if and only if A is row equivalent to the identity matrix, and not every matrix A satisfying Ax = b is row equivalent
to the identity matrix.
В.
The statement is true. Since A is invertible, A 'b =x for all x in R". Multiply both sides by A and the result is Ax = b.
C. The statement is false. The matrix A satisfies Ax = b if and only if A is row equivalent to the identity matrix, and not every matrix that is row equivalent to the
identity matrix is invertible.
D.
The statement is true. Since A is invertible, A 'b exists for all b in R". Define x = A 'b. Then Ax = b.
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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