Problem 1

Determine the value of such that the matrix is the augmented matrix of a consistent linear system.

Problem 2

Consider a linear system whose augmented matrix is

For what value of will the system have no solutions?

Problem 3

Suppose the solution set of a certain system of equations can be described as , , , where is a free variable. Use vectors to describe this solution set as a line in .

Problem 4

Find , and such that corresponds to the given linear system.

Problem 5

Write the system of linear equations

as a matrix equation

Problem 6

Let be a matrix with linearly independent columns. Suppose we know that and satisfy the equations and . Find a solution to .

Problem 7

Solve the matrix equation , where

Problem 8

Solve the matrix equations where

(a).

(b).

(c).

Problem 9

Solve the division problem

Problem 10

Find a set of vectors in that spans the solution set of the equations

Problem 11

Let , describe all solutions of .