Chapter 9 Linear transformations
... The same notation Rn is also often used to denote the set of all n-tuples (row vectors) (a1 , a2 , . . . , an ), but as most of our computations from now on will involve column vectors, for the rest of this module we shall reserve the notation Rn for these. We denote by 0n the column vector which ha ...
... The same notation Rn is also often used to denote the set of all n-tuples (row vectors) (a1 , a2 , . . . , an ), but as most of our computations from now on will involve column vectors, for the rest of this module we shall reserve the notation Rn for these. We denote by 0n the column vector which ha ...
Slide 1
... following statements are logically equivalent. That is, for a particular A, either they are all true statements or they are all false. m a. For each b in , the equation Ax b has a solution. b. Each b in m is a linear combination of the columns of A. m c. The columns of A span . d. A has a pivot po ...
... following statements are logically equivalent. That is, for a particular A, either they are all true statements or they are all false. m a. For each b in , the equation Ax b has a solution. b. Each b in m is a linear combination of the columns of A. m c. The columns of A span . d. A has a pivot po ...
