Problem 1
Use row reduction to solve the following linear system
Problem 2
Let , , and . For what value(s) of is spanned by and .
Problem 3
Let and . Show that the equation does not have a solution for all possible , and describe the set of all for which does have a solution.
For any value of the system forms an inconsistent system, the set of all for which does have a solution must then take the form of .
Problem 4
Let be the linear transformation defined by
(a). Write the Matrix for
(b). Find All Vectors whose Image under is
There is no vector who's image is .
(c). Suppose is in the Range of . Find the Linear Equation Satisfied by , , and
For a solution to exist .
Problem 5
Decide whether the following statements are true or false, and justify your answer.
(a). The Equation Describes a line through Parallel to
False the equation describes a line through the point which is parallel to .
(b). The Columns of Any Matrix Are Linearly Dependent
True there are 5 vectors in , when the number of vectors is more than the space dimension they are always linearly dependent.