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In this lesson, we will learn how to determine the consistency of a system of equations.

Q1:

Find such that is the augmented matrix of a consistent system of equations.

Q2:

If there is a unique solution to a system of linear equations, which of the following must be true of the columns in the augmented matrix?

Q3:

In the given augmented matrix, * denotes an arbitrary number and denotes an arbitrary nonzero number. Determine whether the given augmented matrix is consistent and, if it is consistent, whether its solution is unique.

Q4:

In the augmented matrix denotes an arbitrary number and denotes a nonzero number. Determine whether the given augmented matrix is consistent. If it is consistent, is the solution unique?

Q5:

In the augmented matrix denotes an arbitrary number and denotes an arbitrary nonzero number. Determine whether the given augmented matrix is consistent and, if it is consistent, whether its solution is unique.

Q6:

Suppose the coefficient matrix of a system, of π equations with π variables, has the property that every column is a pivot column. Does the system of equations have a solution? If so, must the solution be unique?

Q7:

Is there a value of that makes an augmented matrix of a consistent matrix? If yes, find the value of .

Q8:

Find conditions on β and π for the following augmented matrix to have no solution, a unique solution, and infinitely many solutions:

Q9:

Find the value of for which the augmented matrix is inconsistent.

Q10:

Suppose a system of linear equations has a 2 Γ 4 augmented matrix and the last column is a pivot column. Could the system of linear equations be consistent?

Q11:

Find conditions on and for the given augmented matrix to have no solution, a unique solution, and infinitely many solutions.

Q12:

Find the solution for the system of equation

If there is no solution, state the reason.

Q13:

Determine the value of π that makes the system of equations have infinitely many solutions.

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