Suppose AB = AC, where B and C are nxp matrices and A is invertible. Show that B = C. Is this true, in general, when A is not invertible? What can be deduced from the assumptions that will help to show B = C? A. Since matrix A is invertible, A -1 exists. O B. Since it is given that AB = AC, divide both sides by matrix A. O C. A=I D. The determinant of A is zero. Write an equivalent equation to AB = AC using A - 1 such that, when it is simplified, the resulting equation will simplify to B = C.
Suppose AB = AC, where B and C are nxp matrices and A is invertible. Show that B = C. Is this true, in general, when A is not invertible? What can be deduced from the assumptions that will help to show B = C? A. Since matrix A is invertible, A -1 exists. O B. Since it is given that AB = AC, divide both sides by matrix A. O C. A=I D. The determinant of A is zero. Write an equivalent equation to AB = AC using A - 1 such that, when it is simplified, the resulting equation will simplify to B = C.
Suppose AB = AC, where B and C are nxp matrices and A is invertible. Show that B = C. Is this true, in general, when A is not invertible? What can be deduced from the assumptions that will help to show B = C? A. Since matrix A is invertible, A -1 exists. O B. Since it is given that AB = AC, divide both sides by matrix A. O C. A=I D. The determinant of A is zero. Write an equivalent equation to AB = AC using A - 1 such that, when it is simplified, the resulting equation will simplify to B = C.
Transcribed Image Text:**Problem Statement:**
Suppose \( AB = AC \), where \( B \) and \( C \) are \( n \times p \) matrices and \( A \) is invertible. Show that \( B = C \). Is this true, in general, when \( A \) is not invertible?
**Question:**
What can be deduced from the assumptions that will help to show \( B = C \)?
**Options:**
- A. Since matrix \( A \) is invertible, \( A^{-1} \) exists. (Selected)
- B. Since it is given that \( AB = AC \), divide both sides by matrix \( A \).
- C. \( A = I \)
- D. The determinant of \( A \) is zero.
**Task:**
Write an equivalent equation to \( AB = AC \) using \( A^{-1} \) such that, when it is simplified, the resulting equation will simplify to \( B = C \).
**Answer Section:**
(Checkbox available for the answer to be marked)
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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